News reports say the woman, who was an event manager, was returning from work in the early hours of New Year's Day when her scooter collided with a car.
Police say the driver of the car, which was carrying four other passengers, kept going for miles, dragging the woman's body along.
Several CCTV videos have emerged that show the body underneath the car.
Road accidents are common in India - and kill hundreds of thousands of people every year - but this particularly horrific case has gained national attention and generated widespread media coverage.
The Indian Express newspaper reported that the woman's body was pulled along the road for almost an hour, and that witnesses made at least five calls to the police before it was located. That this occurred at New Year - when thousands of policemen had been deployed to patrol Delhi's roads - has only added to the questions around the case.
The five men in the car are in police custody and have not made any statements yet.
While the police continue their investigation - the federal home ministry has ordered a swift inquiry - the woman's family says they are stunned.
"My daughter was very cheerful. She loved making Instagram Reels," her mother told BBC Hindi.
The 20-year-old was also the sole breadwinner of her family - her father died some years ago, and her mother had to stop working because of an illness.
"We don't even have money to perform her last rites," her mother said.
IMAGE SOURCE,GETTY IMAGES Image caption, The stretch of road where the woman's scooter was found
The dead woman's family have alleged that she was sexually assaulted because her body was naked when it was recovered - but police have said the post-mortem report does not indicate this.
"All injuries occurred due to blunt force impact and possibly with a vehicular accident and dragging. Also, the report indicates that there is no injury suggestive of sexual assault," according to a statement from senior Delhi police official Sagar Preet Hooda.
He said the provisional cause of death was "shock and haemorrhage due to injury to the head, spine, left femur and both lower limbs".
The police have also said they have located another woman who was riding pillion with the victim when the collision occurred - the second woman fled in fear and is now helping the police.
'Loud music drowned out the screams'
Police said the investigation began after they received two calls on Sunday morning - one regarding a woman being dragged by a Maruti Baleno car, and another after a woman's body was found lying on a road in north Delhi.
They found the car after launching a manhunt and arrested the accused.
The five men have been charged with culpable homicide and causing death by negligence, Commissioner Hooda said.
The accused had borrowed the car from a friend to drive it in the night between 31 December and 1 January, police said.
They added that the accused said they panicked after hitting the scooter and sped off without realising that the woman's body was being dragged along.
Police have said the men will be taken to the scene of the crime to "verify their version of events" and that the car will be examined by a team of forensic experts. Officials also said they would use a dummy to try to recreate what happened.
The accused men claim that they did not hear the victim's screams because they were playing loud music in the car. Reports have said the men were drunk.
Political blame game
The case has also sparked a political row in the national capital.
The Aam Aadmi Party (AAP), which governs Delhi, has been protesting against the federal government over what they call weak security in the city. The AAP does not have any control over the city's police force, which reports to the federal home ministry.
On Monday, party members protested outside Lieutenant Governor VK Saxena's office, demanding his resignation over the issue.
The federal government appoints the lieutenant governor of Delhi.
Image caption, The incident has sparked a political row in Delhi
Speaking to the media, AAP spokesperson Saurabh Bhardwaj also alleged one of the five accused was a member of the ruling Bharatiya Janata Party (BJP) and accused Mr Saxena and police officials of "deliberately concealing this information".
Earlier in the day, Chief Minister Arvind Kejriwal in a tweet demanded that "exemplary action" be taken against the accused, adding that no leniency should be shown towards them even if they had "high political connections".
Home Minister Amit Shah has not directly responded to the AAP's criticism, but he reportedly spoke to the police commissioner and has ordered a swift inquiry into the incident.
Meanwhile, Mr Saxena said that he was overseeing the investigation.
He had earlier said that he was shocked by the "monstrous insensitivity of the perpetrators" and that his head "hangs in shame over the inhuman crime".