The fire erupted on the second and third floors of Jesco supermarket in Al Baraha.
Dubai Civil Defence says firefighters rescued three people who were trapped in the building, after the fire erupted at 11:33 am on Saturday.
It was brought under control by 12:11 pm by rescuers from Al Ras and Al Hamriyah fire stations.
No injuries have been reported.

HH Sheikh Mohammed visits world's largest private dates factory at DIC
UAE reaffirms need for Iran to allow freedom of navigation
UAE President receives written message from Angola leader
UAE, Germany discuss cooperative relations and regional developments
Dubai launches special unit to catch e-scooter, e-bike violators
