The baby was born this month without Covid-19 but with the virus antibodies, the Straits Times newspaper reported on Sunday, citing the mother.
"My doctor suspects I have transferred my Covid-19 antibodies to him during my pregnancy," Celine Ng-Chan told the paper.
Ng-Chan had been mildly ill from the disease and was discharged from hospital after two-and-a-half weeks, the Straits Times said.
Ng-Chan and the National University Hospital (NUH), where she gave birth, did not immediately respond to a request for comment.
The World Health Organisation says it is not yet known whether a pregnant woman with Covid-19 can pass the virus to her foetus or baby during pregnancy or delivery.
To date, the active virus has not been found in samples of fluid around the baby in the womb or in breast milk.
Doctors in China have reported the detection and decline over time of Covid-19 antibodies in babies born to women with the coronavirus disease, according to an article published in October in the journal Emerging Infectious Diseases.
Transmission of the coronavirus from mothers to newborns is rare, doctors from New York-Presbyterian/Columbia University Irving Medical Center reported in October in Jama Pediatrics.