Krogh started his career at small clubs Horne KFUM and Tårs Ugilt, before playing in the topflight Danish 1st Division for Ikast fS. In 1991, the Danish champions from the two years prior, Brøndby, sold their first choice keeper Peter Schmeichel, and Krogh was bought as a replacement. Brøndby did not initially find the success they sought, though Krogh would prove his worth in the domestic league. In the 1995–96 Danish Superliga (formerly known as 1st Division) season, Brøndby was trailing AGF in the league. In the direct match-up of the two teams late in the season, Brøndby was losing 2–3 when Krogh went into the attack at a corner kick, and headed the ball in goal for the 3–3 result that spurred Brøndby on to make a comeback and win the season title. He won four Danish league titles during his career.
On the international scene, Krogh played 66 matches for Brøndby IF, including highlights like the game against CD Tenerife in the 1997 UEFA Cup, when Krogh saved a penalty kick in a game Brøndby won 1–0. One of his best games was the 1998–99 UEFA Champions League match against Bayern Munich which Brøndby won 2–1, and Krogh was subsequently named 1999 Brøndby IF Player of the Year.
Following his retirement as a player in 2002, Krogh got a job in the public relations department of Brøndby IF. After three years in the job, Krogh decided in December 2005 to quit his job and leave the club, citing he wanted new challenges and only wanted to work in a football club if he had direct contact with the sporting aspect. One month later it was revealed that Krogh was hired for Brøndby as a coach for the young goalkeepers in the club, working under head talent scout Kim Vilfort, one of only three people to have played more matches for Brøndby than Krogh.
In January 2008 Krogh became employed in the sponsorship department of Hvidovre IF and manager of the club's reserve team. In 2009 he became new director of Hvidovre IF. He left the club at the end of 2010.