Actress Violet Paley and filmmaker Sarah Tither-Kaplan have recently accused Franco on Twitter of earlier instances of sexual misconduct.
The allegations surfaced after his Golden Globe win on Sunday.
Franco was scheduled to appear during a "Times Talk" panel Wednesday night with his brother, Dave Franco, to discuss their new movie "The Disaster Artist."
However, the Times says they no longer feel comfortable hosting the event.
Franco appeared on "The Late Show" Tuesday night and denied the allegations. He claimed he didn't know what the alleged victims were talking about.