Lindegaard has represented Denmark at under-19, under-20 and senior level. He made his debut for the U-19s in September 2002, and played a 2003 UEFA European Under-19 Football Championship qualification 1–0 win over Switzerland on 13 October 2002. He played a total six youth international games until September 2003.

Born in the Dyrup suburb of Odense, Lindegaard started his career at local Danish Superliga team Odense Boldklub (OB). He made his Danish Superliga debut in a 3–1 victory against Silkeborg IF on 19 November 2006. He made his UEFA competition debut on 30 July 2009, in a 4–3 win over Rabotnički. During most of his time with OB, he was kept out of the team by Arek Onyszko, and he had two loan spells at Kolding FC, where he remained undefeated in the ten league games he got for the team, after it had lost the first four games of the season, and Aalesunds FK, who he would later join permanently. When Onyszko was sacked by Odense in June 2009 due to him being convicted for assaulting his ex-wife, Lindegaard was seen as his replacement.

In 2009, he joined Norwegian club Aalesunds FK on loan and later permanently. In 2009, he won the Norwegian Football Cup with Aalesund. In 2010, Lindegaard was named Goalkeeper of the Year in both Norway and Denmark.

Since early November 2010, he was reported to have become a target for English club Manchester United. On 23 November 2010, it was reported that Manchester United manager Sir Alex Ferguson expected to complete the signing of the player in the “next two or three weeks”. On 27 November 2010, Lindegaard joined Manchester United on a three-and-a-half-year contract for an undisclosed fee believed to be around £3.5 million. He trained with the first team throughout December, but he was unable to play for his new club until the transfer window re-opened on 1 January 2011. Lindegaard was officially registered with the Premier League on 6 January, and assigned the number 34 jersey.

Lindegaard made his senior international debut in a UEFA Euro 2012 qualifier against Iceland on 7 September 2010, which Denmark won 1–0. On 8 October 2010, Denmark faced Portugal in another Euro 2012 qualifier. Early on in the game, with Denmark trailing 2–0, an injury sustained by starting goalkeeper Thomas Sørensen brought Lindegaard into action. He made many saves to keep his team in the game, but conceded a goal in the 85th minute to Cristiano Ronaldo with the match finishing 3–1 in Portugal’s favour. Lindegaard started the following Euro 2012 qualifier against Cyprus, in which he kept a clean sheet as Denmark won 2–0. He was expected to feature for Denmark at the Euro 2012 finals but due to injuries while playing for his club and lack of proper game time post-recovery, his national teammate Stephan Andersen took over after normal second-choice goalkeeper Thomas Sørensen was injured in a pre-tournament friendly against Brazil.

On 1 October 2011, Lindegaard made his Premier League debut for United against Norwich City in a 2–0 win at Old Trafford. He continued his run of clean sheets in his next four appearances in the Premier League, which included a 1–0 home win against Sunderland on 5 November, a 1–0 away win against Aston Villa on 3 December, a 5–0 away win at Fulham on 21 December and a 5–0 home win against Wigan Athletic in United’s Boxing day fixture. His run of clean sheets in the league finally ended on 4 January away to Newcastle United when he was beaten three times in a game that United lost 3–0. A week later, on 8 January, Lindegaard played his biggest game for Manchester United so far, a 3–2 win against Manchester City in the FA Cup. He was chosen again for the starting line-up the following week when United beat Bolton Wanderers 3–0. On 30 January 2012, he damaged ankle ligaments in training, forcing him to miss the game against Stoke City the next day, along with the unwell first-choice David de Gea, meaning youngster Ben Amos played goal. Later in the week, Sir Alex Ferguson revealed Lindegaard would miss the next four-to-five weeks and would not be expected back until the home game with West Bromwich Albion.

On 3 August 2012, Lindegaard signed a new four-year contract with United, keeping him at the club until June 2016. He also took the number 13 jersey made vacant by the departure of Park Ji-sung, who had left the club for Queens Park Rangers.

Since the match against Norwich on 17 November 2012, first-choice goalkeeper David de Gea was sidelined with wisdom teeth problems. Lindegaard was kept in goal for United’s next five games until De Gea was recalled for the Champions League match against CFR Cluj. Lindegaard returned to the first team on 1 December 2012, against Reading in a match which ended 4–3. After the match, he came in for criticism by former United goalkeeper Alex Stepney, who said that he lacks “authority at the back”. After a long period on the bench as an understudy to De Gea, and with United having already secured the Premier League title a month earlier, Lindegaard started in goal for Sir Alex Ferguson’s final game as United manager against West Brom at The Hawthorns; the match finished 5–5. That appearance was Lindegaard’s tenth of the season, thus qualifying him to receive a Premier League winner’s medal.

Lindegaard is one of the few footballers to have spoken out against the intolerance of homosexuality in football and the absence of openly gay players from the professional game. In a 2012 blog entry, he wrote,

Lindegaard married Housewives of Cheshire star, Misse Beqiri, a Swedish model of Albanian roots, in June 2014. They split in 2016. They have a son named Julian.

On 31 August 2015, Lindegaard joined West Bromwich Albion on a free transfer, signing a two-year contract.

On 23 January 2016, Lindegaard joined Championship side Preston North End on loan for the remainder of the 2015–16 season. He made his debut on 2 February where he kept a clean sheet against Derby County. He was voted Man of the Match on his home debut, against Huddersfield Town.

On 2 July 2016, Lindegaard signed a one-year permanent deal with Preston North End after the mutual termination of his West Brom contract.

On 21 September 2017, Lindegaard joined Premier League side Burnley on a free transfer. He made his Burnley debut as a substitute for the injured Nick Pope during the Europa League second qualifying round on 26 July 2018. After making another Europa League appearance against Aberdeen, his contract was not renewed and the club confirmed that he was released by the club.

On 18 July 2019 Lindegaard signed for Allsvenskan side Helsingborgs IF until December 2021. On 19 July 2020 Lindegaard scored the first goal of his career in a 2020 Allsvenskan 2–2 draw against Falkenbergs FF.