A security guard noticed smoke coming from the back of the garage, who then raised the alarm.
The fire is believed to have been caused by a faulty tyre blanket, but the fire then spread to a second set of tyres before being put out.
The two sets of tyres were no longer usable, with Haas submitting a request to the FIA to have them replaced.
The team confirmed that the request had been accepted and that Magnussen would still have his full allocation of 13 sets of dry tyres for the weekend.
Guenther Steiner, Haas team boss, was just thankful that it did not turn into something more serious, like Williams had in Spain in 2012.
“We don’t know what happened yet, because it is all burned,” Steiner told Autosport.
“We cannot jump to a conclusion. I don’t want to put any panic on to what actually happened, because we don’t know.
“I think one security guard saw it and then they all worked together to extinguish it.
“A lucky escape, and it is good that they all worked together and caught it, because if tyres go on fire they are difficult to extinguish.”