In a commentary on Friday, Bashir called the former Alaska governor "America's resident dunce" and a "world class idiot," and suggested she be punished for remarks about slavery by having someone defecate in her mouth.
On Monday, Bashir said he deeply regretted what he said.
"I wanted to take this opportunity to say sorry to Mrs. Palin and offer an unreserved apology to her friends and family, our viewers and anyone else who might have heard what I said," said Bashir, who hosts an hour-long commentary program on the cable network's afternoon schedule.
Bashir's commentary came on the same day that MSNBC suspended Alec Baldwin's weekly talk show for two episodes after the actor was videotaped using an anti-gay slur against a photographer during a New York street encounter.
An MSNBC spokeswoman did not immediately respond to questions Tuesday about whether any further action was being contemplated against Bashir. The former ABC "Nightline" host was on the air for his show on Tuesday. A Fox News representative could not immediately reach Palin for comment.
Bashir had attacked Palin and her "long-diseased mind" after playing video of a speech where she compared the United States' potential indebtedness to China to slavery.
Bashir told the story of Thomas Thistlewood, a former overseer at a plantation who left detailed diaries that described his punishment of wayward slaves. In one case, Thistlewood ordered another slave to defecate in the mouth of the miscreant. In another case, someone urinated in the face of a slave who was being punished.
"When Mrs. Palin invokes slavery, she doesn't just prove her rank ignorance, she confirms (that) if anyone truly qualifies for a dose of discipline from Thomas Thistlewood, then she would be the outstanding candidate," he said.