The body was found after airport security staff were called out on Saturday night to investigate an unattended suitcase in a multi-storey car park serving terminal three, said a spokeswoman for Scotland Yard.
The black canvas case was spotted by a member of the public on an unattended luggage trolley on the third floor of the five-storey car park at 10.40pm.
A Heathrow security officer forced the case open and found the body, with numerous stab wounds to the torso and believed to be clothed only in underwear.
Police were called to the scene, where forensic tests were conducted.
A Scotland Yard spokeswoman said: "The security officer took the suitcase to his vehicle where he forced it open and found a body, coiled up in a foetal position. From the examination of the scene it does not appear that the attack took place in the car park. Inquiries are under way to establish how the case came to be on level three."
Officers conducting the investigation, headed by Detective Chief Inspector Peter Kirkham and Detective John Corrigan, of the metropolitan police, believe the killer carried the body from the murder scene to Heathrow by car, or even on an underground train or bus, before dumping it in the car park.
The police spokeswoman said: "Whoever did this, and wherever it happened, [the person] would be heavily bloodstained."
The victim was about 5ft, of medium build and of Turkish or Moroccan appearance. She had brown eyes and collar-length auburn to blonde hair that was "possibly permed, possibly dyed", the spokeswoman said. A gold chain was around her neck.
She had multiple stab wounds, but police refused to comment further on the number or extent of her injuries. A post mortem examination was carried out at Ealing hospital in west London yesterday morning to establish the cause of death.
Police have been unable to establish the victim's identity and contact her next of kin, and detectives appealed for anyone who knew a missing person fitting her description to contact them.
The discovery of the body caused chaos at Heathrow when the entire area around the short-term car park was cordoned off as police began their investigation. All staff and passengers entering or leaving terminal three, which is used for long-haul flights to America, the Middle East, Asia, Australia and New Zealand, were stopped by police while their identities were checked.
Heathrow is the world's busiest international airport with 60m passengers a year, and July is one of the busiest months for travel, with 1,250 flights a day to more than 200 destinations.
Detectives were understood to be examining hundreds of hours of closed circuit television footage at the airport. They have appealed for witnesses who might have seen someone struggling with a heavy suitcase in the car park, or arriving with the case on foot or by bus, tube or car. The suitcase measures 3ft by 2ft by 1ft, and has a zip, and two plastic clasps. Its four wheels and a pulling handle were missing.
Police also urged people to come forward who may have seen someone with heavily bloodstained clothing, or been at the murder scene, which would also have been covered in blood.
Anyone with information can contact Heathrow police station on 0181-897 1212 or call the Met's Crimestoppers' line on 0800-555 111.
