DAYTON, Ohio—A gunman wearing body armor killed nine people and injured at least 27 in a neighborhood of bars and restaurants here, in the second mass shooting in the U.S. in less than 24 hours and the third in eight days.

The gunman, identified by police as Connor Betts, 24 years old, was killed by police. Among the dead was the suspected shooter’s 22-year-old sister, police said, and her companion was among the injured.

The...