A bus station, a restaurant and another building housing several businesses were targeted, state radio said.
It is not clear who carried out the attacks which come ahead of a planned visit next week by French President Nicolas Sarkozy.
Tension is increasing as the country prepares for elections in August.
The political temperature in Rwanda has been increasing ahead of those polls and opposition parties have complained of persistent harassment, says the BBC’s East Africa correspondent, Will Ross.
But it is not clear whether there are any links between the explosions and the elections.
This month the New York-based Human Rights Watch said there had been an escalation of attacks against opposition party members which, our correspondent adds, did not bode well for the election.
It said this would further undermine democracy by discouraging any meaningful opposition in the elections.
President Paul Kagame’s government is often accused of strongly resisting any political opposition, our correspondent says.
The rights group Amnesty International said this week it was concerned that recent attacks on opposition parties were part of a wider pattern of intimidation and harassment, aimed at discouraging and discrediting opposition groups.
Source: BBC News