With 1km of the 6km course destroyed, a new climb will be cut by trail-pixies led by Whiteley. The MTB races are scheduled for next Friday and Saturday.
Mount Parnitha is known for its combustible flora, a large forest fire occurred in the same area last month.
Friday's fire is believed to have been caused by a worker using a wire-cutting tool, Olympics officials said.
Greek newspapers report that the workman was interviewed by police, and later released.
Training will start on the course on Monday after TV technicians have laid new cabling, sections of which were damaged by the fire.