The Brazilian was testing for the first time this year after Spanish teammate Fernando Alonso had spent Tuesday and Wednesday in the F150.
The Italian team said on their website (www.ferrari.com) that Massa pulled over when the car suffered an oil leak caused by a broken clamp.
"Unfortunately the lubricant ended up on the exhausts which led to a small fire breaking out and that caused some damage to the car.
"The mechanics immediately set to work on repairing the damage, but it is unlikely that the car will be back on track much before 3.00 in the afternoon."
Massa was sixth overall last season, with double world champion Alonso runner-up, and has plenty of pressure on him to improve after enduring continuing speculation about his future with the team.
The first race is in Bahrain on March 13.