Body parts were found in the club leading officials to believe the explosion may have been the work of a suicide bomber.
The second explosion happened at a popular Ethiopian restaurant in Kampala.
At least three Americans travelling with a church group from Pennsylvania were among the wounded.
The group bans music, dancing and sports and has recently condemned Uganda for its peacekeeping efforts in Somalia.
One anti-terrorism expert told Eyewitness News that this was not a random act because Uganda also hosts Somali soldiers trained by the United States.
If confirmed it would be the first time ever al-Shabab has carried out attacks outside of Somalia. less dangerous.