The incident took place last night at 11:30 PM when Pooja, mother of the child, flung the baby soon after she delivered him at her home in Ajmal Palace, they said.
The accused was married to a diamond worker Jignesh Shapariya in February this year.
Police Inspector M N Parmar said that probably Pooja threw the baby boy because she didn't want a child within a year of marriage.
Complainant Vasubhai Sabalpara, one of her neighbours, brought the incident to light. However, it is unclear why she threw the child.
According to police, neighbours and eye-witnesses called the ambulance service and admitted the new-born to SMIMER hospital, run by the Surat Municipal Corporation but the child died.
Police have registered a murder case under Sec 302 of the Indian Penal Code and are investigating the exact reason behind the step taken by the mother.
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Pooja has been admitted to SMIMER and her condition is being monitored, they said, adding that women police are at the hospital.
Her family members are being interrogated, police said.