Perez, who also took pole in last year's race here, topped the leaderboard with a best lap of one minute 28.265 seconds.
Ferrari's Charles Leclerc was second, 0.155sec behind Perez, but faces a 10-place grid drop, leaving Fernando Alonso to start on the front row in his Aston Martin.
Seven-time world champion Lewis Hamilton could only post the eighth-quickest time but his teammate George Russell was fourth fastest and will start third, alongside the Ferrari of Carlos Sainz.
Lance Stroll in the second Aston Martin and Alpine's Esteban Ocon will be on the third row of the grid.
Verstappen, who won the opening race in Bahrain at the start of the month, had dominated practice, topping the board in each of the three sessions.
However, in Q2 he reported to his team "I have a problem" before adding "it's almost not accelerating".
The Dutchman pulled up and will start on the eighth row of the grid.
