Perez, who won the famous Monaco race last year and has a reputation as master of the Formula One street race, lost control of his car at Turn 1 and collided heavily with the barriers.
Perez will start at the back of the grid Sunday at a race in which overtaking opportunities are famously limited because of the tight and twisty nature of the circuit.
Verstappen leads Perez by 14 points after his win at the Miami Grand Prix and will see a big opportunity to open up that lead if he can qualify highly.
Verstappen went quickest in Saturday's final practice.
Perez's crash has also opened up the door to the likes of Ferrari and Aston Martin -- both have also looked quick this weekend -- to grab a spot on the front row of the grid.
Ferrari's Carlos Sainz went quickest in opening practice on Friday, although Verstappen was quickest in the second session.