KABUL—Doctors Without Borders closed its only hospital in northern Afghanistan after it was hit by U.S. airstrikes that the aid organization called a war crime, while officials launched multiple investigations into the attack.

The international medical-aid organization, also known by its French name Médecins Sans Frontières, said 12 staff members and 10 patients in the Kunduz hospital were killed and much of the facility destroyed in the assault shortly after 2 a.m. Saturday.

It...