The teenager was hit by a Volkswagen Polo while crossing the A452 Chester Road in Erdington with his family just before 6.50pm.
Police named the teenager as Mason O'Grady as they confirmed a woman has been arrested on suspicion of causing death by dangerous driving and failing to stop.
Mason was taken to hospital but died a short time later, West Midlands Police said.
In a tribute to Mason, his family said: "Mason was a handsome, kind, loving and genuine boy with a heart of gold.
"He would do anything to make you smile and he brought happiness and joy to the life of everyone he met.
"Yesterday whilst out walking with his family he was hit by a car as he crossed the road. As a family we are asking for any witnesses to come forward to help us understand why this happened to our beautiful, kind spirited boy.
"Mason, we will love you always."
A black Polo was found around two miles away on Eachelhurst Road.
A 28-year-old woman was arrested remained in police custody for questioning on Monday morning.
Collision investigators were sent to the scene on Chester Road, while forensics teams were also seen photographing the Polo on Eachelhurst Road.
Detective Sergeant Alan Hands, from the West Midlands Police collision investigation unit, said: “We are still trying to establish how this tragic incident has happened and anyone who has information and hasn’t yet spoken to an officer should call us on 101.
“This is a parent’s worst nightmare and it’s impossible to imagine their grief, but specialist officers will be supporting them as our investigation continues."
The crash happened at around the same time that a motorcyclist was left critically injured when he was involved in a crash with a car in Oldbury.
Anyone with information on either incident can contact collision investigators on firstname.lastname@example.org, via Live Chat at www.west-midlands.police.uk 8am - midnight, or by calling 101 anytime.
Information can also be given to Crimestoppers anonymously on 0800 555 111. Quote log number 3376 of April 12.