Emergency services were called to the blaze at Old Salty’s on Byres Road at 8.42am on Friday.
Flats on the first and second floors of the three storey building were evacuated.
The Scottish Fire and Rescue Service said two people were treated for “minor smoke inhilation” following the ground floor fire.
Byres Road was closed to all traffic between Highburgh Road and Great Western Road.
A spokesman said: “The Scottish Fire and Rescue Service was alerted at 8.42am on Friday, June 8 to reports of a kitchen fire within a business premises on Byres Road, Glasgow.
“Operations Control immediately mobilised a number of fire engines and an aerial unit to the three-storey building, where firefighters are currently tackling a fire on the ground floor.
“Two casualties are being treated by the Scottish Ambulance Service for minor smoke inhalation, and the first and second floor flats have been evacuated.
“Crews will remain at the scene until the area is made safe.”