The first blast hit a bus carrying about 50 people in the upmarket Defence area of Karachi at about 7.40 am local time.
A lady doctor and a sub-lieutenant of the navy were killed in the attack, a naval spokesman told the media. Over 15 people were injured in the attack.
Another bus carrying naval employees to work was hit by the second blast in Baldia Town area about 10 minutes later.
TV news channels reported that at least one person was killed and 15 others were injured in this attack. The condition of four persons, including the driver, was described as serious.
Sharfuddin Memon, the Interior Adviser of Sindh province, confirmed that three people were killed in the attacks.
Both bombs were detonated by remote control, Special Superintendent of Police Raja Umar Khattab told the media.
In the Defence area, the bus was targeted with an explosive device planted in a motorcycle. Footage on television showed a mangled motorcycle lying near the bus.
The second bus was targeted with a bomb hidden in a pile of stones near the roadside in Baldia Town.
Initial reports on state-run PTV had described both attacks as suicide bombings. The injured were taken to a naval hospital.
Large contingents of paramilitary and armed forces personnel cordoned off the sites of both blasts. Members of the bomb disposal squad scoured the sites for clues.
No group claimed responsibility for the attacks. Pro-Taliban militants are usually blamed for such bombings.