Wolfhagen took part in the first official Danish national team game, played at the 1908 Summer Olympics, as he scored four goals in the 9-0 victory against France B from his favoured position of forward. He scored another four goals in the second game of the 1908 Olympics, a 17–1 defeat of the France A team, the biggest ever win of the Denmark national team. In the final game of the tournament, Denmark lost 2–0 to Great Britain, thus winning silver medals. Four years later, Wolfhagen scored one goal in Denmark's three games at the 1912 Olympics, before they were once again defeated by Great Britain in the final. He ended his national team career in October 1917, having scored 14 goals in 18 national team games.