Bhattercharjee, 53, was last seen on July 10 leaving rehearsals at the Royal Court Theatre in Sloane Square, London, at about 6.15pm.
"He left on Wednesday in good spirits but didn't make it to rehearsals the next day," said a spokeswoman for the Royal Court.
The actor, who also uses the name Gautam Paul Bhattacharjee, sent a text to his girlfriend at around 9pm that night but has not been heard from since, reported Daily Mirror.
Police described his disappearance as "totally out of character".
Bhattacharjee from Redbridge, north-east London, who also starred in films The Best Exotic Marigold Hotel, White Teeth and Dirty Pretty Things, was due to appear in black comedy Talk Show this week.