Born in Bremen, Meisner briefly worked at a steel foundry before training as a radio operator with the Luftwaffe's Fallschirmjäger (paratroopers). After the war, though he was interested in a career in sculpture and painting, in 1948 he switched to drama and studied under Gustaf Gründgens at Düsseldorf's State Conservatory, where he also got his first job at the local Schauspielhaus.