The boy suffered injuries to his back and hand when a shotgun was fired at a house in the Eastfield area of the city just before 4pm on Good Friday.
The attack is thought to have been a case of mistaken identity.
A 17-year-old boy and a 24-year-old man have since been arrested on suspicion of wounding.
Interactive map of the shooting:
The youngster was inside his family home in Ashbourne Road when a group of men opened fire at the property. The men are thought to have been chasing a group of people before mistakenly firing at the house.
No other injuries have been reported from what was the second shooting in the West Midlands in two days, after a man was shot dead on a Birmingham street on Thursday.
'Three masked men'
A local resident, who asked not to be named, said three masked men ran across a pedestrianised area at the end of Ashbourne Road into Deans Road and fled on foot.
The witness said: “I heard two loud bangs and then three guys wearing balaclavas came into the street and I saw one of them put a gun into a bag.
“I think two of them were wearing all white. They had what looked like a dark sports bag and they put the gun in that, then ran off.
“They went up the street and I’ve heard that a woman chased them in a car.
“I didn’t realise at the time that anybody had been shot, let alone a six-year-old.
“I didn’t hear any screaming or anything. We’re all just hoping he’s OK.”
Detective Inspector Rod Rose said the motive behind the attack was not yet known, despite it appearing to have been a targeted incident gone wrong.
"These arrests are a significant step forward in our investigation which continues at pace," he said.
"It’s a shocking incident where someone has opened fire with a shotgun in broad daylight.
"The motive of this attack remains unclear and we’re working hard to try and understand what happened earlier today.
"We have extra officers, including armed officers, in the area as we’ve increased patrols to support and reassure the community during this concerning time.
"If anyone was in the area at the time and saw what happened I would urge them to get in touch."
Bank Holiday peace broken
A police helicopter was hovering over the city as armed officers rushed to the scene after the shots were fired on Good Friday afternoon.
A stretch of Ashbourne Road, which is made up of terraced and semi-detached houses and connects Old Heath Road with Deans Road, remained cordoned off late on Friday as police searched the surrounding area and spoke to local residents.
Specialist search teams scoured Ashbourne Road and Deans Road, while firearms officers and forensic teams were also at the scene.
Many people had been out enjoying bank holiday sunshine on the first day of the Easter weekend when the gunfire broke the peace.
One neighbour, who did not want to be named, said: “We just came home from a day out and saw this.
“We heard what happened through my mum who heard gunshots.
Scroll down for updates from the scene
“I have my grandson with me, he’s only seven, so it’s scary.
“When it’s on your street, I just can’t believe it.”
Eighteen months ago a 14-year-old boy was stabbed in Ashbourne Road in the middle of the day, while in 2008 a 13-year-old boy was mauled by a dog nearby.
One resident, who also wished to remain anonymous, said they had never let their children play on the "problem street".
“It’s a shocking street, we always have problems on this street," they said.
“We have been looking to move from here, it’s always been a problem street but the police don’t do enough to stop it."
Another neighbour added: “The kids were playing in the garden and heard bangs.
“It’s a bad street, I’ve lived here all my life and I hate it, I want to move.”
Reporter Liam Keen was at the scene:
A number of detectives are also on the scene. It’s a very large operation from the police.— Liam Keen (@LiamKeen_Star) April 19, 2019
It’s important to make clear at this point that it’s not known which house was involved.— Liam Keen (@LiamKeen_Star) April 19, 2019
Anyone with information is urged to contact West Midlands Police on 101 or via the force website between 8am and midnight.
Alternatively Crimestoppers can be contacted anonymously on 0800 555 111.