Monteith, 31, was found dead in a hotel room in Vancouver on Saturday. He was in Canada to visit his mother, the Hollywood Reporter said.
"It was done today, and that included taking samples for toxicology," B C Coroner Services spokeswoman Barb McLintock said.
McLintock said the results of the initial autopsy should be available Tuesday. If the results prove inconclusive, additional tests may be required to establish the cause of death for Monteith. Foul play was ruled out in Montheith's death by the Vancouver police.
The actor had struggled with drug addiction in the past and had recently completed a stint in rehab but McLintock did not speculate on whether a drug overdose may have caused the rising star's death.
McLintock added the autopsy and toxicology testing has been fast-tracked, given the global media attention surrounding Monteith's death.