Michael Mann was sent to the hospital after he accidentally shot himself in the leg at a Los Angeles gun range ... TMZ has learned.

A source tells TMZ ... the "Heat" director had been apparently trying to holster his weapon at the gun range around 4 PM when the firearm went off.

He was later transported by an ambulance to a local hospital.

The LAPD confirms the incident to us ... cops and the LAFD responded to The Range LA after reports of the shooting.

They say the victim -- who had no intention of harming himself -- was injured during a training accident when he accidentally discharged a firearm into his own leg.

We've reached out to Michael's rep for comment ... so far, no word back.