Poulsen started his career in the local football club, Ikast KFUM. He made his professional debut in the Danish Superliga for FC Midtjylland on 1 December 2016 in a game against Silkeborg IF, where he played the whole game on the left back.[2]
Poulsen won the 'Academy Player of The Year' award at FC Midtjylland for the 2017–18 season.[3]
Borussia Mönchengladbach
After a great 2017–18 season for Poulsen with 12 games played for the first team, Poulsen was sold to Borussia Mönchengladbach for 34 million Danish kroner (€4.5 million) which could further increase to 50 million kroner (€6.7 million). This made him the most expensive teenager in Danish football history.[4] Poulsen signed a five-year contract with the German club.
Austria Wien
On 3 January 2020, it was announced that Poulsen had been loaned to Austria Wien of the Austrian Bundesliga for the remainder of the season.[5]
On 8 February 2021, Poulson moved for a second time to Austria Wien, on a loan deal until the end of the season.[6]
FC Ingolstadt
On 19 August 2021, it was announced that Poulsen had been loaned to 2. Bundesliga side FC Ingolstadt 04, until the end of the season.[7]
AaB
At the end of June 2022 it was confirmed that Poulsen had returned to his homeland, signing a deal until June 2026 with Danish Superliga side AaB.[8]
Silkeborg IF
At the end of August 2023, Poulsen joined Silkeborg IF on a one-year loan deal.[9] After the season, Silkeborg IF and Poulsen made the deal permanent, with him signing a 3-year contract.[10]
