Kwale area police chief Jack Ekakuro said three people approached the crowded bar and hurled a grenade toward customers before speeding away on a motorbike.
"We had an explosion at the bar and about 10 people were injured," he said.
Officials said at least one of the victims had suffered serious injuries and had undergone surgery at a nearby hospital.
It was not immediately clear who was behind the attack, but Ekakuro told reporters that “it cannot be anything else but a terrorist attack. A grenade is a not a maize cob that any village boy can handle and throw around at will.”
The Kenyan government has in the past put the blame on Somalia’s al Qaeda-linked al Shabaab insurgents, who have demanded the withdrawal of Kenyan troops who have joined African peacekeepers fighting the group in Somalia.
Kenya has been the scene of multiple terrorist attacks since the country sent its military to Somalia in 2011 to fight the al Qaeda-allied Islamic rebels of al Shabab. In September, the group claimed responsibility for an attack on the Westgate Mall in the capital, Nairobi. At least 67 people were killed in that attack.
(FRANCE 24 with AP and REUTERS)