The attempt was discovered on Saturday morning after the man, in his 30s, and his wife arrived at the airport from Egypt.
An investigation was launched after an X-ray machine showed the child was hidden in the hand baggage.
The baby boy, who is just a year old, had no visa, passport or official documents allowing him to enter the UAE.
A police official told Gulf News: “When customs officials saw the baby inside the bag at the X-ray scanner, they were stunned.
“This machine is very dangerous for anyone, let alone a baby in a bag to pass through.