The Mexican lost the rear of his C33 coming through Turn 3 and slid sideways into the wall on the outside of Turn 4.
The incident caused red flags to briefly fly while the car was recovered and transported back to the Sauber garage.
A number of other drivers also had off-track moments in FP3 - including McLaren's Kevin Magnussen, Lotus's Romain Grosjean, Caterham's Marcus Ericsson and Force India's Sergio Perez - but all escaped without damage.
Gutierrez's incident comes two weeks after he tagged the wall and spun while running eighth in Monaco - which also scuppered Sauber's hopes of scoring their first points of the season.
The team is currently 10th in the constructors' championship, ahead of Caterham only by virtue of Gutierrez's 12th-place finish in Australia.