The 39-year-old comedian admitted that it had been inappropriate to post the gag so soon after Friday's (November 4) tragedy, which claimed the lives of seven people and left 51 injured.
The joke read: "An (sic) couple married for 66 yrs died within 3 days of each other. That's nothing. My grandparents died on exactly the same day.... car crash."
After facing a backlash from fans believing that he was making fun of the incident, Carr replied: "Very bad timing by me. The joke was obviously not about recent tragic events. Apologies if any offence caused."
The joke has since been removed from his official Twitter profile.
Carr recently said that he never feels guilty for making offensive jokes.
His 8 Out Of 10 Cats co-star Jon Richardson told Digital Spy last week that he doesn't believe in upsetting people for the sake of comedy.