The fire is just west of U.S. Highway 101 and was reported at about 5:30 a.m.
The San Jose Fire Department said at about 7:45 a.m. in an update that crews were still on scene battling the blaze with aerial hose attacks. They are keeping a safe distance in anticipation of potential collapse of the building.
The fire was prevented from spreading to other structures.
No injuries were reported at that time.
The fire department asked drivers to continue to avoid the area.
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