The person who was killed was carrying a piece of luggage that contained the bomb, police commissioner Mathew K. Iteere said. It was not immediately clear if it was a suicide attack, Iteere said.
Most of the wounded were Ugandans traveling home for Christmas, Red Cross official Nelly Muluka said.
Al-Shabab, Somalia's most dangerous militant group, has threatened to carry out more attacks on Uganda and Burundi, the two nations that contribute troops to the 8,000-strong African Union force in Mogadishu. Twin bombings in July in Uganda claimed by al-Shabab killed 76.
A security official in Nairobi said Uganda and Burundi have been on high alert since early November that they would be targeted by al-Shabab. The official spoke on condition of anonymity because he was not permitted by his organization to be identified.
Muluka put the toll of people wounded at 39. Iteere said one person was killed and 26 wounded.
The explosion took place just as people were boarding a bus line called the Kampala Coach, a line that serves major cities in East Africa, including the capital of Uganda, Kampala. Windows in the front of the bus were shattered but the bus did not sustain major structural damage.
Iteere said the explosion happened just as the person carrying the luggage was about to be screened. It is common in Kenya to screen passengers for weapons that could be used to carry out potential hijackings in rural areas.
"I felt like I was hit by an electric shock," said Jack Wachira, 49, who escorted a friend to the bus station. "When the particles hit my leg, I thought I stepped on electrical wires. Then I heard the explosion."
Vincent Sekatte, a police spokesman in Uganda, said that threats against his country "have been on for some time."
"The terrorists have always threatened to hit during Christmas season. Tomorrow we are issuing a serious warning to the public about the threats," Sekatte said. Yahoo! News