Police said a “serious blast” occurred at around 9 pm (1800 GMT) on Saturday at a grilled pork joint in Komamboga, a northern Kampala suburb popular with roadside diners.
Museveni said he had been briefed that three people left a plastic shopping bag at the scene that later exploded, killing one person and injuring five others.
“It seems to be a terrorist act but we shall get the perpetrators,” Museveni said in a Twitter post on Sunday.
He said investigators were still combing the bomb site and more details would be released later, including advice for the public about “dealing with these possible terrorists”.
“The public should not fear, we shall defeat this criminality like we have defeated all the other criminality committed by the pigs who don’t respect life,” Museveni said.
The blast occurred about two hours after the start of a nationwide dusk-to-dawn coronavirus curfew.
Security forces rushed to the scene, which was cordoned off as the bomb squad picked through the site.
On October 8, the Islamic State group claimed its first attack in Uganda, a bomb attack against a police post in the Kawempe area, near where Saturday’s explosion occurred.
In a statement issued through its communication channels, the group claimed a unit from its Central Africa operation had detonated an improvised explosive device that resulted in injuries and damage to police infrastructure.
No explosion or any injuries were reported by authorities or local media at the time, though police later confirmed a minor incident had occurred without providing further details.
However in the following days, both the UK and France updated their travel advice for Uganda, urging vigilance in crowded areas and public places like restaurants, bars and hotels.
“Terrorists are very likely to try to carry out attacks in Uganda. Attacks could be indiscriminate, including in places visited by foreigners,” stated the updated advice from the UK.
In 2010, twin bombings in Kampala targeting fans watching the World Cup final left 76 people dead.
Somalia’s Al-Shabaab militant group claimed responsibility for the blasts at a restaurant and at a rugby club.
The attack, the first outside Somalia by the insurgents, was seen as revenge for Uganda sending troops to the war-torn country as part of an African Union mission to confront Al-Shabaab.