Khan's baby boy was born on May 27.
"BMC officials have received a birth report with details that a baby boy was born on May 27 to parents listed as Shah Rukh Khan and Gauri Shah Rukh Khan at Masrani Hospital for Women in Andheri," The Times of India reported.
"The child was born at 34 weeks of pregnancy and weighed 1.5 kg at birth," Brihanmumbai Municipal Corporation (BMC) executive health officer Dr. Arun Bamne told the newspaper.
"We have received from Masrani Nursing Home a birth report, which has to be mandatorily filed by nursing homes and hospitals to register every birth in the city," Bamne said.
The boy was taken from Masrani Hospital to Nanavati Hospital. He was later shifted to Breach Candy Hospital, reports said.
It is believed that the baby has been discharged from Breach Candy Hospital and he is currently with the Khans.
Khan and Gauri tied knot in 1991 after long years of friendship.
They have two children - son Aryan (15) and daughter Suhana (13)