Police said the explosions on Monday night were caused by home-made pipe bombs. Two of them had been put into taxis, and the third went off in a taxi park.
Police say they have arrested four people in connection with the explosions.
No one has claimed responsibility. Police spokesman Asuman Mugengyi told the BBC that two of those arrested were amongst the injured, but they had refused to go to hospital, which aroused the police's suspicion. The police spokesman said the worst blast occurred at Kampala's main taxi rank. The police has not so far found a political motive for the bombings. Attacks The BBC correspondent in Kampala says the bomb attacks are the latest in a series of explosions, which have been occurring intermittently in Kampala since 1997.