KYIV, Ukraine—Residents of Ukraine’s capital were weathering missile strikes and a cyberattack on a mobile-network operator that authorities called Russian efforts to sow chaos and sap national morale.

Ukrainian air defense shot down 10 ballistic missiles over Kyiv early Wednesday morning, according to Ukrainian officials. The falling debris hit residential buildings, a kindergarten and a hospital, injuring more than 50 people and damaging the municipal water system.