The fire late on Friday damaged the players’ boots and kit, as well as medical and technical equipment. No one was injured and the reason for the fire was not yet known, the club said.
It said the area had been sealed off, adding in a statement: “Due to the damage incurred... and the lack of usable match and medical equipment, Basel is unable to play the away match against Thun on Saturday."
The league had approved the postponement and a new date would be found, Basel said.
Basel are fourth in the standings, 18 points behind leaders Thun, who have 71 points from 32 games.