The brief blaze on top of the car while it was in the garage between Q1 runs was swiftly extinguished.
Gutierrez was able to rapidly rejoin the session and went on to qualify 14th.
Sauber's engineering chief Tom McCullough said it was not yet clear where the fuel vapour came from.
"There was a little bit of fuel vapour that caught fire, presumably from a breather or something to do with the connector - but I'm not sure of the cause," he told AUTOSPORT.
"There was no damage to the car, it just burned in the air.
"It looked impressive but it was very little fuel.
"It happens every now and again with a hot car on a quick refuel. No harm done."
Sauber qualified in the top 10 again at Suzuka as Nico Hulkenberg took seventh.
"He got all we had out of the car today," said McCullough.
"The grid was very, very tight from the front to the back of Q2.
"Williams and Force India were strong, Toro Rosso a bit slow in that first sector but it was very, very tight and Esteban was unlucky just to miss out on Q3 by a tiny margin after doing a very good job all weekend.
"Nico squeezed everything out of it. Again we felt there was a bit more to come in Q3 so we decided to have a go and in the end seventh is much better than 10th."