KYIV—Russia sent waves of explosive drones to strike cities across Ukraine in the largest attack since last winter that likely marks the start of a fresh campaign aimed at demoralizing and dislocating Ukrainians.

Ukraine’s military said it intercepted all but one of 75 Shahed drones overnight, most of which were targeted at Kyiv. Authorities in the capital said five people were slightly injured, including an 11-year-old child, and several buildings damaged.