Police launched a murder investigation after the discovery, on the A4136 between Monmouth and Coleford.
A Gloucestershire Police spokesperson said a member of the public reported suspicions to police about a vehicle due to its manner of driving at around 10.30pm.
When the vehicle was located by police, two suitcases were found to contain human remains and two people - a woman in her twenties from Birmingham and a man in his thirties from Wolverhampton - were subsequently arrested. They remain in police custody.
Investigating officers believe there is one victim, a woman, and forensic examinations are ongoing to confirm her identity.
Senior Investigating Officer DCI John Turner said: "The nature of this incident is distressing and we're working around the clock to fully understand what has happened.
"Someone's life has been lost and our priority is to identify the victim and get answers for her family.
“Searches have taken place in the surrounding area for evidence gathering and contrary to media reports no remains have been found as part of these searches.
“Our Major Crime Investigation Team is working in collaboration with the West Midlands Police homicide team to carry out further enquiries.”