Meißner made his professional debut for Hamburger SV in the 2. Bundesliga on 1 March 2021, coming on as a substitute in the first minute of second-half stoppage time against his former club FC St. Pauli. The away match finished as a 1–0 loss for Hamburg.[5]
On 30 January 2022, Meißner joined Hansa Rostock on loan until the end of the season.[6] On 27 July 2022, he moved on a new loan to Viktoria Köln.[7]
On 4 July 2023, Meißner moved to Dynamo Dresden on a two-year deal.[8]