The bomb, packed with nails and shrapnel, targeted a pork restaurant on the outskirts of the capital, police said on Sunday.
Information gathered indicated that three men, disguised as customers, visited the restaurant, placed a polythene bag under a table, and left moments before the explosion, police said.
The explosion killed a 20-year-old waitress and injured three people, two of whom were in critical condition, police said, adding all indications suggest an act of domestic terror.
President Yoweri Museveni said the attack “seems to be a terrorist act”.
In 2010, the Somali Islamist militant group al Shabaab killed dozens of people in Kampala in a bomb attack, saying it was punishing Uganda for deploying troops in Somalia