The defending champion only managed to qualify fourth as compatriot Lando Norris took pole for McLaren
The 36-year-old Briton topped the standings after both Q1 and Q2 but could not replicate his dominance when it mattered most.
Hamilton collided with the pit wall in the last few minutes and then spun into the wall again when he went back out on track as he suffered two crashes in a matter of moments.
Carlos Sainz secured a place on the front row for Ferrari as he qualified second, with another Briton, George Russell, rounding out the top three.
And Hamilton, whose world title rival Max Verstappen is set to start from the back of the grid after opting to replace his engine, was devastated with the mistakes he made.
Speaking after qualifying, the seven-time champion said: “Ultimately I’m incredibly disappointed in myself. Up until then, I was in a groove, I was really in the zone.
“I’m really sorry for all the team that are here and back at the factory, because obviously that’s not what you expect from a champion. It is what it is, and I’ll do my best tomorrow to try and rectify it.”
Hamilton still has a strong chance of winning the grand prix, a victory that would take him back ahead of Verstappen in the title race.
“The guys up front have got good pace, and it definitely won’t be easy," han la til. “I’m just going to say my prayers and hope that the car can be fixed, and it’s hopefully okay for tomorrow.
“These things are sent to try us, and I feel terrible right now. But I’ll turn it into a positive, and try to do the best. But you’ve got a Brit on pole, which is great, so congrats to Lando.”