Hans Montag was on the West German hockey (field) team at the 1976 Montréal Olympics that won its match for fifth place, 9-1, against Spain, although he did not play in that match. Montag earned 100 international caps. Domestically, he played with Kölner KHT Schwarz-Weiß, helping them to win the West German title in 1976, alongside his brother Joachim, whose son Jan-Marco Montag also became a hockey player. Kölner HTC Blau-Weiß was his home club where Hans Montag later became a long-time sports administrator.