Klein was born in Berlin, during the time of the Weimar Republic, to an affluent Hungarian Jewish family, that returned to Budapest, before the outbreak of World War II.

After serving in the Israeli navy, he joined Maccabi Tel Aviv, with which he played in more than 160 games, through 1964.

With Israel's senior national team, he played at the 1952 Summer Olympic Games, and at the 1954 edition of the FIBA World Cup.

He also coached the German League club Saturn Köln, and he won another Israeli State Cup title with Hapoel Tel Aviv.

In 1983, he unexpectedly announced his appointment as the head coach of the senior West German national team.