Museveni said three people entered the eatery in a suburb of Kampala on Saturday evening and left a plastic bag whose contents later exploded.
He provided no more details in a series of Twitter posts but vowed to "get the perpetrators." Police said in a statement that at least one person had died and seven others were injured in the blast.
The eatery is a normally busy place, frequented by commuters.
Police, who have sealed off the scene, said a bomb squad is investigating the explosion, which for many revived painful memories of a deadly bombing in 2010 that killed over 70 people in Kampala. That attack was carried out by members of the Somali Islamic extremist group al-Shabab, which said it was retaliating against Uganda's deployment of peacekeeping troops to the Horn of Africa nation.
There haven't been similar blasts in recent years, and Uganda is relatively peaceful.
But the U.K. government updated its Uganda travel advisory earlier in October to say extremists "are very likely to try to carry out attacks" in this East African country.
"Attacks could be indiscriminate, including in places visited by foreigners," that advisory says.
Museveni, who has held power since 1986, is a U.S. ally on regional security. He was re-elected in January in polls the opposition said were neither free nor fair.