Rinku Das (27), whose husband had deserted her, had sold the baby through a local fixer Madhab Saha, SP Sabyasachi Raman Mishra said.
Saha too was detained, the SP said.
The baby was allegedly bought by one Apu Guha, who resides in Rajberi under Amdanga Police Station area in North 24 Parganas district, Mishra said.
Steps were being taken to recover the baby, he said.