WASHINGTON—Chinese military personnel are targeting American flight crews in the skies over the east African nation of Djibouti using a high-powered laser in what amounts to a new show of Chinese harassment of the U.S. military at a time of heightened tensions between the nations, according to Pentagon officials.

The incidents bolster longstanding U.S. concerns about China’s decision to establish its first overseas military outpost close to the largest U.S. military base in Africa.

The...