"A rocket hit a building in the Afshar district [of Kabul] resulting in three people being slightly injured according to the preliminary information," the source said.
The TOLO news broadcaster later reported citing witnesses that two more rockets landed in the area.
No militant group has claimed responsibility for the incident so far.
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The attack came just two days after a blast near the Kabul airport killed up to 23 people.
The tensions in Afganistan are growing, as various militant groups, including the Taliban movement, continue to fight against the central government. According to the UN Assistance Mission in Afghanistan (UNAMA), the number of civilian casualties in Afghanistan in 2018 was the highest in any six-month period since 2009.