Qatar defeated the host nation 27–22 in the final at the Al-Khalifa Sports Complex in Isa Town.
Japan defeated Saudi Arabia 25-16 in the earlier bronze medal match.
It marked its first medal since a bronze in the 2010 edition in Beirut.
All four semi-finalist have now qualified for the 2017 World Championships in France, while fifth-placed Iran secured a berth at the final qualification tournament.