A plainclothes policeman said he had fired a warning shot in the backyard of the residential block before shooting at the man in an attempt to stop him escaping.
The suspect died immediately at the scene with a bullet to the back of his head, but the officer later said he meant to shoot him in the legs.
An autopsy was carried out on the body in Munich over the weekend.
The Bavarian Office for Criminal Investigation (LKA) has taken over the case and charged the officer with manslaughter through negligence, police said in a statement on Monday.
Investigators are currently interviewing witnesses and fellow officers who saw the incident unfold.
The 33-year-old was wanted for drug offences. A warrant for his arrest was issued several months ago.
It is not clear whether he had been armed or had threatened the officer.
Around 50 people joined a protest on Saturday in Burghausen against "police violence" after the killing.