Gunnar Nielsen (born 7 October 1986) is a Faroese footballer who is currently a free agent. Nielsen most recently played for Premier League champions Manchester City.

Born in Tórshavn, Nielsen was signed by Blackburn Rovers for a "small" but undisclosed fee on 2 July 2007 from BK Frem. Nielsen, who was on trial with Rovers in May, told the club website: "I am very pleased - it is a massive chance for me just to develop. "I'm glad the manager and staff believe in me and I won't let them down." He joined Motherwell in the Scottish Premier League on a six-month loan on 8 August 2008. He returned to Blackburn on 30 December 2008.

He signed for Manchester City on a two-and-a-half-year contract, and shortly afterwards he joined Conference National side Wrexham on loan. He made his debut in a 1–0 defeat to Histon on 28 March. He was suspected to have sustained a thumb injury during a game against Oxford United in April, meaning he returned to City for a scan, which confirmed the suspected injury.

Nielsen made his Premier League debut on 24 April 2010 as a substitute for injured Shay Given in the 76th minute during Manchester City's stalemate against Arsenal. As a result Nielsen became the first Faroese footballer to play in the Premier League. In the summer of 2010, he signed a contract extension with Manchester City that runs until 2012.

He joined League One team Tranmere Rovers on loan until January 2011 on 23 July 2010. He made his debut for Tranmere in a 2–1 defeat by Oldham Athletic on 7 August, After picking up an injury on international duty, he spent over three months out, before returning to the first team at Tranmere in December 2010.

He was released by Man City at the end of the 2011/12 season. However, weeks later he rejoined the Manchester City squad, but was again released by the club after signing former England international Richard Wright on transfer deadline day.