Sheikh Mukhtar was the son of Chaudhry Ashfaq Ahmed (who was a railway police inspector and born in Karachi, British India; now Pakistan) Chaudhary Ashfaq Ahmed intentionally got transferred and  migrated to Delhi. Sheikh Mukhtar was born on 24 December 1914 in Delhi.
His father wanted his son to join the Police or Army on a higher rank, but Sheikh Mukhtar was keenly interested in theatre. One of his acquaintances from his area started working in a theatre company, so Sheikh Mukhtar also moved to Kolkata and joined the company.