Saudi Arabia has revoked the citizenship of Osama bin Laden’s son, Hamza, a move that comes as the State Department designated him as an emerging leader in the extremist group his late father founded, al Qaeda.

The State Department Thursday offered a reward of up to $1 million for information about Hamza bin Laden, citing audio and video recordings he has released since 2015 calling for attacks on the U.S. and its allies. The State Department declared Mr. bin Laden a Specially Designated Global Terrorist in 2017, freezing...