Police said the woman, now in her 50s, said that she wanted to make amends with her past and "cleanse" herself of the infant's death and hiding the facts for so long, Gulf News reported Wednesday.
The woman said that she was 13 years old when her family married her to someone and she later became pregnant. When she had her baby boy, she said that she was too young to understand enough about caring for him, the Gulf News said.
When she told an acquaintance about her situation and lack of maternal instinct, she said he suggested she strangle the baby.
"I then went on with the suggestion and killed my baby," she said.
She told police her husband and relatives didn't suspect anything different when she told them he died of natural causes, the newspaper said.
She told police the acquaintance died many years ago and that her husband also died.
The woman, whose nationality and name were not reported, said she wanted to be punished for the murder because she was haunted by the boy's face for years.
Police said the woman would be in custody while her case is investigated by police and reviewed by proper authorities.