Haugaard began his career with Akademisk BK before moving to Danish Superliga side Midtjylland in December 2011.

Haugaard was born in Sundby and played in the youth teams at Tårnby Boldklub and Brøndby IF before he signed with Danish 1st Division side Akademisk BK in 2010.

[9] Following a long-term injury to first choice goalkeeper Jack Butland, Haugaard was given his Premier League debut on 2 April 2016 in a 2–2 draw with Swansea City.

[13] On 7 January 2017, Haugaard joined EFL Championship club Wigan Athletic on loan for the remainder of the 2016–17 season.

[16] Haugaard was heavily criticised by Latics caretaker manager Graham Barrow following a 2–1 defeat at Brighton & Hove Albion on 17 April, describing the goals he conceded as "Sunday League" and admitting that he is only playing Haugaard because of the terms in the loan deal with Stoke.