Brøndby IF On 25 October 2012, Hjulsager signed a two-year extension to his contract which tying him to the club until summer 2015. Hjulsager made his debut at the age of 18, starting as a
right winger in the first match of the season, a 1–1 home draw against
FC Vestsjælland on 21 July 2013. He crowned his debut with a goal which made him the second youngest goalscorer in the history of
Brøndby IF. On 22 August 2013, Hjulsager signed a new four-year contract until summer 2017. He ended season 2013–14 with 23 appearances and four goals despite the fact that he formally belonged to Brøndby IF’s under-19 squad. His performance made UEFA named him the Danish league "One to Watch" in the annual Danish season review due to his impressive ability to read the game combined with his superior technique, incredible pace and offensive mindset. Hjulsager started the season with a slot among the starting eleven in a 9–0 home victory against the San Marino side
Juvenes/Dogana in the
UEFA Europa League qualification.
Celta On 31 January 2017, Hjulsager signed a three-and-a-half-year contract with
La Liga side
Celta de Vigo. On 31 January 2018, Hjulsager was loaned to
Segunda División side
Granada CF until the end of
the season.
Oostende On 12 July 2019, it was confirmed that Belgium side
Oostende has secured the signing of Andrew Hjulsager from Celta Vigo. The Spanish club reserved a right to a percentage of any future sale of the player.
Gent On 11 June 2021, Hjulsager signed a four-year contract with
Belgian Pro League club
Gent. The deal was reported to be around €2 million.
Vejle Boldklub On 29 June 2025, Hjulsager returned to his home country to play for
Danish Superliga club
Vejle on a three-year deal. ==Career statistics==