The young woman, who was described as of Turkish or Moroccan origin, was found by a security guard. The suitcase measured 3ft by 2ft by 9in and was dumped on the third floor of the car park at Terminal 3 at about 10.40pm on Saturday.
The unidentified woman, who was in her 20s and about 5ft tall, was crammed into the case, coiled up in a foetal position, said a Scotland Yard spokesman. She had multiple stab wounds, although a post- mortem examination held yesterday morning was inconclusive as to the cause of death.
Detectives said that murderer would be "heavily bloodstained". They believe the woman was stabbed away from the airport and later dumped in the case. There is no suggestion of sexual assault.
A guard put the locked case into a security vehicle and forced it open after it was reported as suspect by a passer-by. A spokeswoman for Heathrow airport said that the guard would be offered counselling.
The handle and wheels of the black canvas case were missing, and police appealed to anyone who may have seen someone dragging a heavy case at the airport.
It was not known how the body arrived in the car park. It may have been taken by car, on foot or by Tube or bus.
After the discovery, the car park was cordoned off by police as detectives began an investigation. The site was reopened yesterday morning.
Passengers and staff leaving Terminal 3 during the early hours of the morning had their identities checked to ensure the killer did not flee the country. Terminal 3 is used for long-haul services to the United States.
Police have appealed for help from anyone who knows someone missing who fits the description of the woman. She was of medium build, had collar-length auburn or blond hair, possibly permed and dyed, and brown eyes. She was lightly clothed and wearing a gold chain with circular links but no other jewellery, although her ears were pierced.
Police have also asked anyone who was in the car park and saw anything suspicious, such as someone struggling with a heavy suitcase or covered in blood, to contact them on 0181-897 1212 or to call Crimestoppers on 0800 555111.