His lap was a mere 0.015 quicker than Honda's championship leader.
Maverick Vinales was third fastest lap for the factory Yamaha team but was subsequently handed a three-place grid penalty for 'riding in an irresponsible manner' at the end of the session.
The pole was the second of Quartararo's first season in MotoGP, following on from becoming the youngest ever pole-sitter in the top category at the Spanish Grand Prix at Jerez in May.
The Frenchman won the second tier Moto2 race in Barcelona last year.
Petronas Yamaha's Franco Morbidelli moved up to third place, with fellow Italians Valentino Rossi on the other works Yamaha and Ducati's title contender Andrea Dovizioso lining up fourth and fifth.
The top 12 riders on the grid were separated by less than a second.
Spaniard Jorge Lorenzo, last year's winner in Barcelona for Ducati and now Marquez's team mate, qualified 10th.
Marquez leads Dovizioso by 12 points in the standings after six rounds of the 19-race championship.
(Reporting by Alan Baldwin, editing by Pritha Sarkar/Nick Mulvenney)
