Police say an unidentified person tossed an explosive device thought to be a grenade into the club, where it exploded, Standard Digital News reported.
No arrest has been made so far, said Agrey Adoli, a regional police commander.
"Our experts are there to know who threw the grenade," Adoli said.
No one claimed responsibility for attack immediately, the Kenya Broadcasting Corp. reported.
The injured were in stable condition at a hospital, Adoli said.