A fuel cell arrangement with a membrane electrode assembly is provided which comprises a cathode, an anode and a membrane arranged between the cathode and the anode, with an active area essentially predetermined by the membrane electrode assembly, and with a sealing structure laterally assigned to the membrane electrode assembly. The sealing structure comprises a sealing tongue extending into or over an edge region outside the active area for axially covering in a gas-tight manner a media channel formed in an adjacent bipolar plate and located in the edge region. A unit cell for a fuel cell stack with such a fuel cell arrangement is also provided.