The child has been identified as Cruz Jovanovic and his father is Christian Jovanovic.
Police say the child was taken from a northeast Calgary parking lot around 8 p.m. Friday evening after an altercation between the man and the boy's mother.
"It's not very often that we will issue an Amber Alert," said Duty Insp. Michael Watterston. "In this particular case, we have a situation where the father, the biological father, forcibly took his child from the mother. He is not entitled to have custody of that child and that's one of our primary concerns.
"And also, while the child was forcibly removed from the vehicle, we believe he did strike his head on a part of the vehicle. We're concerned for the child's well-being in that respect."
Watterston said the father doesn't have basic amenities to look after the child, such as food and diapers, and is believed to be on foot.
He said the man is known to police.
"We are aware of Mr. Jovanovic; he has had contact with police in the past, but not related to this situation."
Jovanovic, 40, is described as five-foot-seven, 143 pounds, with brown eyes and brown hair.
He has several tattoos, including a clown on his right forearm, a black panther on his left shoulder, a devil head on his left forearm, and a large Egyptian eye on his neck.
He was last seen wearing a grey T-shirt and blue jeans covered in white paint.
The boy was wearing all green clothing, including a lime green tank top.