South Wales Police said the incident happened at about 17:50 BST on Friday near to Court Road, Barry, and involved a black Renault Clio
The child was taken to the University Hospital of Wales in Cardiff.
Anyone with information is asked to call 101.

Chastain, who is now retired from the sport, said she hoped it would help "change things for the positive".
She joins a number of sporting figures helping to research long-term effects of concussion on competitors in sports.
CTE, a degenerative disease, has been found in athletes with a history of repetitive brain trauma.
Chastain, 47, announced on Thursday she would be donating her brain to Boston University, which is leading studies into the effects of multiple concussions and chronic traumatic encephalopathy (CTE).
"It's scary to think about all the heading and potential concussions that were never diagnosed in my life, but it's better to know," she said, speculating about her own experience of head injury during her football career.
CTE is associated with symptoms such as memory loss, depression and progressive dementia.
No female athletes have been found to have suffered from CTE, the New York Times reports, though this may be because the sample size is too small. The disease has been found in a number of male sports stars - including many former American football players.
CTE cases can only be diagnosed after examination of the brain post-mortem.
Chastain's decision follows that of her team mate, Cindy Parlow Cone, who has also decided to donate her brain.
Both women have been calling on football regulators to introduce regulation preventing children under the age of 14 from heading the ball.
Research into CTE has thrown the spotlight on several sports, including American football, horse-racing and rugby in recent months.
A Hollywood film about the effects of concussion on National Football League stars was released last year, starring Will Smith.
In February, it was revealed Ken Stabler, one of the most celebrated quarterbacks of all time, had been suffering from the disease.
Chastain became well known for scoring America's winning goal in a penalty shoot-out against China in the final of the 1999 Women's World Cup.
Images of the football star kneeling on the pitch in her black sports bra, fists clenched, swept around the world, becoming an iconic image for women's football.

A 5ft x 3ft (1.5m x 1m) void appeared on Whitworth Street on Sunday, resulting in the road's closure between Princess Street and Oxford Street.
A section of the busy Mancunian Way has been closed since August, after two holes opened up. Replacement sewer pipes are being installed.
United Utilities said sewers underneath Whitworth Street have not been damaged.
"Non-urgent" roadworks in other parts of the city have been suspended until after Christmas in order to relieve congestion caused by Mancunian Way's partial closure.
Councillor Pat Karney, city centre lead for Manchester City Council, said Whitworth Street should be repaired in time for Monday's evening rush hour.
He described the appearance of the latest hole as "incredibly unfortunate".
"The council has placed a moratorium on all non-urgent roadworks, but this is the last thing we needed at the moment," he added.
He said the council will investigate why the city is being "blighted" by holes.
A 40ft (12m) wide sinkhole opened up in August on the Mancunian Way after heavy rainfall, while another hole appeared a month later.
A 10-year-old child has suffered serious injuries after being hit by a car in the Vale of Glamorgan.
[NEXT_CONCEPT]
US football star Brandi Chastain, who shot to fame in the 1999 Women's World Cup, has pledged to donate her brain to the Concussion Legacy Foundation.
[NEXT_CONCEPT]
Motorists in Manchester are being frustrated by the appearance of yet another hole in a city-centre road.