According to Rahimi, the first blast targeted a bus of a university at 07:50 a.m. local time, killing one person and injuring 10 others.
Rahimi also said that the targeted bus was carrying Burhanuddin Rabbani Education University lecturers and staff members in the western edge of Kabul city.
It was a sticky bomb attached to the bus, the official further said.
The second blast in a span of 20 minutes occurred in the same area after police and rescue team arrived, injuring seven people including a local journalist and five security personnel, eyewitnesses said.
The third blast, also in the same area but caused no loss of life.
No group has claimed responsibility for the bombings yet.
Over the past months, Afghanistan, especially Kabul city has witnessed waves of terror attacks, claimed by the Taliban group and the Islamic State (IS) outfit opposing the government.