There was no immediate claim of responsibility, but Kenya has blamed similar attacks on the al-Qaida-linked Somali group al-Shabaab, which killed at least 67 people at the Westgate shopping mall in Nairobi last September.
There have been a string of attacks since then.
“A grenade was thrown at passengers,” the Mombasa county commissioner, Nelson Marwa, said.
“The attackers were riding on a motorbike and lobbed the grenade at the crowd of people at the bus terminus.”
More than 20 people were wounded.
Guards at the seaside Reef hotel said they had prevented attackers from entering, but the suspects threw a bag with an explosive device into the compound. The blast ripped the roof of one building and part of its wall collapsed.
At the bus terminus, victims were lying in a pool of blood and the road was littered with shattered glass from a bus.
“I didn’t see who threw the object, but I heard a loud explosion before I fell to the ground. I then felt my legs go numb,” said local supermarket worker Halima Sidi, 26, as nurses bandaged her wounds.
The Kenyan coast’s large Muslim minority, many of whom feel marginalized by the government, has been a fertile recruitment ground for Islamist militant networks.
Kenya sent soldiers into Somalia in 2011 to try to drive out al-Shabaab, which it sees as a threat to its own borders and security.
President Uhuru Kenyatta has said the tourism sector was “on its knees” as a result of attacks by the militants, who want Kenyan troops out of Somalia. Kenyatta has rejected their demand.
Mombasa is a draw for tourists as well as a major port for the east African region.