Kamui Kobayashi crashed heavily in the closing stages of the first day, losing the rear of his car at high-speed through Turn 3 and hitting the barrier.
The resulting impact caused damage that proved impossible to repair overnight, meaning the team are unable to run on the second day.
"Having assessed the damage to chassis CT05-03 after Kamui's accident yesterday in the final half hour of day one, we have decided not to run on day two," a team statement said.
"While obviously not ideal, this ensures the team can now focus on the next Grand Prix in Monaco, starting next week"
Caterham's test driver Robin Frijns had been scheduled to take over from Kobayashi for the second day.
The Dutchman has made three test appearances for Caterham so far this year, and made his first appearance on a Grand Prix weekend on Friday in Bahrain.
Kobayashi apologised immediately after his mistake, saying: "Unfortunately in the last half hour I went off in Turn 3 on run 22 and hit the barriers pretty hard. There is quite a lot of damage to the car so I'm sorry for the guys in the garage who now have a long night ahead to fix the car.
"The only good thing is that it was at the end of the day after we'd got through most of the run plan."