ABC is pulling the plug on Christmas with the Backstreet Boys … a late decision that comes immediately on the heels of Nick Carter being accused of sexual battery.

The band’s special, “A Very Backstreet Holiday,” was set to air on ABC next week, and featured all 5 singers — Nick, Brian, Howie, AJ and Kevin — but the network has canceled the airing … TMZ has confirmed.

The special was shot last month in L.A., and, at this stage, would be complete and ready to air. ABC isn’t offering any explanation for the last-minute cancelation, but with the announcement coming less than 24 hours after the lawsuit against Carter … it’s pretty clear.

TMZ broke the story … Shannon Ruth sued the singer Thursday for sexual battery, saying she was 17 back in 2001 when was allegedly invited on his tour bus and given alcohol.

According to legal docs, Ruth — who’s autistic with cerebral palsy — was then sexually assaulted by Carter … and when she threatened to tell people about what he did, he allegedly called her a “r******* little bitch” who no one would believe. She says she contracted HPV after the incident and is now seeking damages.