Passenger Michelle McDuffie said people onboard felt a thud when the plane touched down after a flight from Long Beach, but nobody thought there was an emergency until the crew shouted for everyone to exit on the inflatable slides.
McDuffie saw the burning tires when she was on the ground.
"I thought, Oh I wish I had gotten my bag off. But I was just happy that I wasn't hurt," said McDuffie, 33, of Mission Viejo.
The plane appeared to experience trouble with its brakes, the airline said in a statement.
The 87 passengers were taken to the terminal by buses, said airport spokeswoman Gina Swankie, who couldn't immediately confirm how many tires had blown on the plane.
The nature of the injuries weren't immediately available, but five people were taken to a hospital, Swankie said. An elderly woman was seen being loaded onto a stretcher, complaining of neck pains.
Everyone was "able to slide down that slide and walk over to our triage," Sacramento Fire Department Capt. Jonathan Burgess said.
Rob Vanatta, 32, was waiting for the Jetblue flight when someone announced on the terminal intercom that it was delayed.
"Then they came back on the intercom, sounding surprised or in shock, and said 'I'm not sure how to tell you this, but the wheels caught fire upon landing and the emergency slides had been deployed,"' Vanatta said.
Vanatta ran to the window to see what happened and saw passengers standing on the runway near the plane, surrounded by fire trucks.
"My friend and I were able to rebook to a flight out of Oakland, so we're driving there now," he said.
The incident was being investigated by the National Transportation Safety Board.
Associated Press Writers Juliet Williams in Sacramento, and Trevor Hunnicutt, Marcus Wohlsen and Jason Dearen in San Francisco contributed to this report.