Tribeka Lounge caught fire on Monday afternoon after a deep fryer burst into flames in the kitchen.
Staff and customers at the bar located on Banda Street in the central business district hastily vacated the building.
Speaking to the Star, National Disaster Management Digital Officer Peter Kung'u said the staff were able to contain 90 per cent of the fire before the Nairobi county firefighters arrived.
"There is no cause for alarm. Workers used fire extinguishers to contain the flames before firefighters arrived," he said.
Kung'u said when they arrived at the scene, there was dense smoke, but fortunately, the fire had not spread.
The management is yet to determine the extent of the damage.