Born inØstervrå,Vendsyssel, Mæhle started playing football with local club Østervrå IF and moved to theAaB youth academy as a 12-year-old.[3] At the age of 19, Mæhle was promoted into the first team squad on 10 June 2016 and also signed a full-time senior contract with AaB.[4] He made his debut for AaB on 7 August 2016.[5] He started on the bench, but replacedThomas Enevoldsen in the 89th minute in a 2–1 victory againstFC Nordsjælland in theDanish Superliga.
On 11 November 2016, Mæhle earned a new contract until 2020.[6] In April 2017, AaB confirmed that they were in negotiations with a foreign club about Mæhle.
On 9 May 2017, AaB confirmed that they had sold Mæhle to Belgian clubRacing Genk for an undisclosed fee, starting from 1 July 2017.[3] He was signed to succeed right-backTimothy Castagne, who had moved toAtalanta. Mæhle made his debut for Genk on 29 July 2017 in the first league match of the season againstWaasland-Beveren as a substitute forAmine Khammas. In his first season with the club, he was not a fixed starter, competing withClinton Mata for his position. In his second season, after Mata's departure toClub Brugge, he won a permanent starting position. That season, Mæhle grew into a key player in the Genk starting eleven. At the end of the season, Genk won theBelgian championship.
On 11 September 2019, Mæhle extended his contract until June 2023.[7]
Genk announced on 22 December 2020 that Mæhle had signed forAtalanta on a five-year contract for a fee of €10 million. His transfer was made official on 4 January 2021.[8] He made hisSerie A debut for Atalanta on 6 January in the club's 3–0 win overParma.[9] On 28 February, Mæhle provided an assist in Atalanta's 2–0 win overSampdoria.[10] Mæhle scored his first goal for Atalanta in a 6–2 Serie A victory overUdinese on 9 January 2022.[11]
In August of 2023, Mæhle joined VfL Wolfsburg for a fee of reportedly around €12 million.[12] On 6 September 2023 he scored his first goal for the club in a 2–1 win against1. FC Union Berlin.[13]