Ummad Rushdi, 31, the boyfriend of the child's mother, was arrested around 2:30 a.m. Wednesday in York, Pa.
That child, 7-month-old Hamza Ali, has not yet been found.
In case the baby is still alive, police released a photo of him on Wednesday morning to aid in the search.
Police say the investigation began after they received a call from the infant's mother Tuesday night saying she, Rushdi and the child had been visiting Rushdi's parents in Upper Darby over the weekend.
She said Rushdi, whom she has known for three weeks, took the baby early Sunday morning and that she believed he was heading back to York, where they both live.
Police believe the boy was taken from the home before the mother was awake.
"Apparently they were sleeping inside 6604 Chestnut Street. Rushdi was in the room, by himself with the baby. There was some type of interaction where the baby died and Rushdi did not want to share with the mother that the baby had died so he drove the baby out of that location," Chitwood said, but added this was preliminary information as the investigation begins.
Police believe the child was killed in Upper Darby and was taken to an area near York, Pa. or Columbia, Pa.
Chitwood said Rushdi's brother told police he believed that Rushdi killed the child and buried him in a field in York.
When police found Rushdi in York, he tried to run out the back door of a home, Chitwood said. Officers arrested him and found the car he was driving abandoned, he said.
When Rushdi was arrested, he had $800 in cash, a knife and handcuffs in his possession, Chitwood said.
Rushdi is in custody, facing kidnapping and other charges. Chitwood said he was not being cooperative.
Rushdi is now in the custody of Upper Darby police. He arrived in an unmarked car around noon Wednesday.