Det Con Corbett has been with the police force for 18 years
Det Con Catherine Corbett, 39, of Solihull, suffered head injuries in the incident in Hayes, west London, and remains critical after surgery.
Firearms officers arrested a 41-year-old man in Birmingham on suspicion of attempted murder of the West Midlands Police officer.
A woman aged 32 has also been held in London in connection with the case.
Police were expected to continue questioning the man and woman on Saturday.
The man, who was picked up in Bordesley Green area of Birmingham, was initially held at a police station in the city and was taken to London overnight.
Det Con Corbett was trying to arrest a man when he drove off and knocked her over at 0800 GMT.
The police officer underwent surgery at Charing Cross Hospital on Friday afternoon and her family are at her bedside, West Midlands Police said. The hospital is a specialist neurosurgery centre.
Car abandoned
Police said the officer had been in London for the previous two days as part of a fraud investigation.
She was with other officers at the Sheraton Hotel, near Heathrow Airport, when the suspect, who was accompanied by a female, drove up to the entrance.
The officers parked in front of and behind his car but he drove off, carrying two officers along on the bonnet for a short distance.
Det Con Corbett was knocked down as a suspect drove off
As he reversed, the open passenger door hit Det Con Corbett, who was in plain clothes.
He then crashed into a black Ford Focus, damaging its front bumper and bonnet, as he made his escape. Detectives said they had been hunting the man for about 12 months.
A woman later presented herself to officers during the day and is being questioned.
Two other officers suffered minor injuries and shock and are being treated at Hillingdon Hospital, west London.
The suspect escaped in a blue Peugeot 207, which was later found abandoned in nearby Harlington Road.
Ervis Topalli, who works at a nearby car-wash, said the car's wheels span as it sped away from the car park before it stopped and a tall, blonde woman got out and ran away.
'Very good officer'
He said: "I didn't think anything of it at the time. I thought it was just a car wheel spinning.
"But then I heard the noise of the brakes and the flap of the flat tyre and I wondered what was going on."
He said: "When she saw me she looked away and started going faster. She went off in the direction of the Ibis Hotel. I didn't see the man but police told me that he was driving."
Det Con Corbett, who has served with the West Midlands force for 18 years, is single, has no children and is a serving member of the economic crime team.
She received a commendation for outstanding work in 1993.
Assistant Chief Constable Gareth Cann said: "Cathy is an experienced police officer and a very good police officer. She is also a good person.
"She is held in high regard and is well-respected by the rest of her team."
DC Catherine Corbett was seriously injured in the incident.  

A 42-year-old man and a woman in her thirties have been arrested after a police officer was left critically injured after being hit by a car as she tried to make an arrest in west London this morning. 

Police are treating the incident as attempted murder.

Detective Constable Catherine Corbett of West Midlands Police was trying to arrest a man at Sheraton Hotel, near Heathrow Airport when the suspect escaped by car and left the officer with head injuries. She was in London as part of a fraud investigation. 

The man was arrested by firearms officers in Birmingham and will be taken to London for questioning. The woman has been held after she contacted the police.

Speaking about Corbett, Assistant Chief Constable Gareth Cann said, "Cathy is an experienced police officer and a very good police officer."

Police have appealed for anyone with any information to contact the Metropolitan Police Incident Room on 020 8358 0400 or Crimestoppers anonymously on 0800 555 111.