Pc Gareth Phillips, aged 42, was being treated in intensive care today where his condition was said to be stable.
The officer was knocked down and driven over while trying to arrest a suspected car thief in Birmingham on Saturday.
The update on his care came as a man appeared in court charged with attempting to murder the police constable.
The veteran officer, who has served with the force for almost 20 years, had surgery over the weekend.
Although his condition is not life-threatening, the force said the longer term prognosis was as yet “unclear”.
His family have spoken of their gratitude for the messages of support which flooded into West Midlands Police since he was injured.
In a statement, Pc Phillips’ family said: “We are grateful for all the messages of support that we’ve had from the police and members of the public.
“Gareth is still very poorly and faces a long battle to recover.
"What happened on Saturday demonstrates the dangers that officers face every day.
"We’d ask for people to respect our privacy now while we as a family support Gareth over the weeks and months ahead.”
A police BMW was hijacked in Moorcroft Road, Moseley, at around 4.45pm and reversed into the officer, knocking him down, before driving over his body as he lay pinned under the vehicle.
Mubashar Hussain, 29, of no fixed address but previously of Sherwood Road, Hall Green, was arrested in the Sparkbrook area short time later.
Hussain, who is charged with a total of 13 offences including attempted murder, appeared in the dock of Birmingham Magistrates’ Court on Monday flanked by security officers.
He spoke only to confirm his name, age and address and was told the offences were so serious they must be sent to the city’s crown court.
Two car theft charges relate to a black Range Rover stolen on Friday, and a blue Range Rover Sport, taken on Saturday.
It is alleged Hussain stole a Range Rover Sport at about 4.30pm on the day the officer was injured and another Range Rover, taken the previous day.
Hussain, wearing a white t-shirt, appeared alongside 24-year-old Ahsan Ghafoor, formerly of Fulham Road, Sparkhill.
Ghafoor, wearing a grey t-shirt, is accused of taking both Range Rovers, dangerous driving, and driving the Range Rover Sport without a licence and without insurance.
Both were remanded in custody to appear before Birmingham Crown Court on September 9.