Officers believe the 48-year-old victim may have been hit by a vehicle in Drumbathie Road, Airdrie, early yesterday morning.
Emergency services raced to the scene at around 12.25am and the man was taken to Monklands Hospital.
However, he died a short time later.
Sergeant David Stenhouse, from the Road Policing Department, said: "Inquiries are continuing to establish the exact cause of his death.
"However, at this time, we believe that the victim may have been struck by a vehicle which didn't stop.
"Officers are carrying out inquiries in the local area and studying CCTV footage in an effort to gather more information.
"I would urge anyone who may have witnessed this incident take place, or who may have information that will assist this police investigation, to come forward.
Police believe the vehicle involved may have been damaged and have urged anyone with information to come forward.
Sergeant Stenhouse added: "The driver of the vehicle concerned may be unaware that they had struck someone.
"I would urge anyone who may have been involved in an incident or were driving between 11.50pm on Sunday and 12.25am on Monday in Drumbathie Road to contact police.
"The vehicle involved, may have sustained damage, and I would ask anyone who has noticed such a vehicle to contact police.
"If someone has seen a car parked in an unusual place, or has any suspicions then please come forward."
Anyone with any information is asked to contact Police Scotland on 101.