One explosion occurred near parliament, the other near the city’s police headquarters
There are fears that the blasts could have killed or injured people. An NTV Uganda reporter said he saw pieces of flesh scattered along the road.
The cause of the explosion is unknown, with Ugandan authorities blaming it on Islamist militants.
Ugandan troops are part of the African Union peacekeeping force in Somalia fighting the al-Shabab-linked al-Qaida rebel group.
Last month, the Islamic State group said it was behind an attack on a bar in Kampala that killed a 20-year-old waitress.