The blaze is believed to have started on one of the stalls at 14:10 GMT Thursday, with hundreds of people leaving as it was tackled.
Traders returned at 15:00 but a Swansea council spokesman said an investigation into its cause needed to take place before it reopened to the public.
Fire officers were also making sure it is smoke free.
Swansea Market has been closed for the day after it was evacuated because of a fire.