Emergency services were called to Thimblemill Road, in Smethwick, after receiving reports of a collision involving a car and pedestrians at around 10.40am on Monday.
The VW Golf did not stop at the scene – and was abandoned later on. Two men aged, 22 and 33 years old, were arrested after a short foot chase
One child required treatment at the scene, while the woman suffered minor injuries. The second child was uninjured. All three were taken to hospital.
The road, near the junction of St Mark's Road, was closed for some time while emergency services were at the scene – but had reopened by 2.30pm.
A West Midlands Police spokesman said: "Thimblemill Road in Smethwick was closed this morning [Monday] after a hit and run at the junction of Hales Lane.
"A mother and her two young children were taken to hospital with serious injuries after being hit by a car just after 10.30am.
"Their condition is not considered life-threatening but very distressing for those involved.
"The VW Golf did not stop and was spotted by officers. It was subsequently abandoned and two men aged, 22 and 33, were arrested after a short footchase. They remain in police custody on suspicion of failing to stop at the scene of a collision.
"Enquiries on on-going and anyone with information who hasn’t yet spoken to us should contact us."
A spokesman for West Midlands Ambulance Service said: "We were called at 10.42am on Monday to reports of a road traffic collision involving a car and pedestrians in Thimblemill Road, Smethwick.
"An ambulance, paramedic officer and critical care paramedic attended.
"Three pedestrians, a woman and two young children, were reportedly involved in a collision with a car.
"All three patients were assessed by ambulance staff on scene; one child was uninjured, the woman suffered minor injuries and the second child required treatment on scene before all three were conveyed to hospital for further checks."
Former hospital worker, Vicky Cempura, was sat in her living room when she heard a "massive bang" and ran outside. She has spoken out about the moment she rushed to help the woman and two children.
The 47-year-old said: "I was sat watching the telly with my daughter Courtney, all I heard was a massive bang.
"We flew outside and could hear screaming. There was a woman, a little boy and a baby in a push chair.
"I got bottles of water and towels and chairs. My daughter held the baby and I tried to help the woman and boy.
"It was just instant reaction, my daughter phoned an ambulance, she was really good.
"It was scary as my daughter has a baby the same age and it could have been her walking down the street."
She said the woman and children were stood by the bus stop. She said the woman sustained mouth injuries, while the boy had a head injury and the baby had a "bump on his head".
Vicky, a former hospital theatre support worker, added that they were standing near an elderly woman, who was not hurt, but she thought was in shock.
"The car crashed into my hedge as the bus stop is outside my house," she added.
"The car was coming from St Mark's Road.
"My husband got the car registration number as it drove off and hit other cars down the street.
"It was just a shock and something I don't want to see again. It could have been a murder scene.
"The road is terrible, it's really dangerous, they're always speeding up and down it."
A woman walking past with a pram, who did not wish to be named, said she had seen the road closed off by emergency services in the morning.
She added: "It's really awkward when the bus stops at the bus stop as the cars have to go around it onto the wrong side of the road, it's too narrow."
A driver, who did not wish to be named, said he had to be diverted at about 12.30pm when he was passing but the road had reopened by 2.30pm.
Anyone with information can call West Midlands Police on 101, quoting log number 1745 of July 12.