The woman, identified as Rukaiya, allegedly abducted Mohammad Ali on October 23 by diverting attention of his parents Afsana Banu and her husband Haidar Khan, they said.
Police said that the woman, who introduced herself as Rukaiya to the parents of Ali, appeared to be a beggar.
"The couple runs a tea shop in Unava. The suspected woman has been visiting that shop since last one week and befriended the couple. Khan told us that Rukaiya picked their son and started playing with him on that day. As soon as the couple got busy, Rukaiya vanished with Ali," Unjha police sub-inspector V S Thakor said.
This is the third such incident of kidnapping in Gujarat during the festive season of Diwali.
On October 21, a six-month-old girl was allegedly kidnapped by two persons dressed as monks on the outskirts of Morbi town.
In another case, an eight-month-old boy was allegedly picked up by a woman from a lodge in Chotila town early today in Surendranagar district.
