Demarquis Elkins, 17, and a 14-year-old boy, whose name was not released because of his age, were arrested Friday in Brunswick, Ga., and charged for the Thursday shooting, CNN reported.
Sherry West, 41, the baby's mother, said she was walking to the post office, pushing her son, Antonio, in a stroller, when one of the teens allegedly approached her and asked for money.
"A boy approached me and told me he wanted my money, and I told him I didn't have any money. And he said, 'Give me your money or I'm going to kill you and I'm going to shoot your baby and kill your baby,' and I said, 'I don't have any money,' and 'Don't kill my baby,'" West said
The boy tried to grab her purse, West said, then allegedly started shooting. West was shot in the leg, "and then, all of a sudden, he walked over and he shot my baby in the face," she said.
West said the younger boy was standing behind the older one during the incident.
Police carried out an extensive search for the suspects that involved a SWAT team and a helicopter search and ended with the arrest of Elkins and the other boy, ABC News reported.
"We are still investigating the motive, but we are trying to turn every stone to make sure we get a motive," said police chief Tobe Green.
Green said police were executing search warrants for three locations and that the gun used in the incident has not yet been recovered.
Both of the suspects have been charged with first-degree murder.
2014: The Year in Music [PHOTOS]