The one fatality reported to date occurred in the north of the city when a bomb hidden in a pushcart hit a bus carrying government workers.
The largest number of casualties was caused when a remote-controlled mine hit an Afghan army bus in the center of the capital. Some 40 people traveling on the bus were hurt, most of them lightly.
A third blast went off in the east of the city, but no one was reported hurt.
Afghanistan has seen a surge of violence blamed on Taliban insurgents this year. Attacks in Kabul are rare, but on July 4 two similar bomb attacks injured several people.
Overnight, coalition forces killed about 35 militants during a raid on a Taliban compound in the southern province of Helmand.
(compiled from agency reports)