The arrested include the woman's mother, police said.
The accused were identified as Kamlesh Bhanushali (29), Mahesh Bande (24) and the woman and her mother Shanta Banerjee (45), they added.
On October 9, Manpada police had received information that body of a baby was lying near a building.
When they went to the spot, they found that the body was packed in a blue coloured bag and the throat of the new born was slit, said police.
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"On the night of October 9, the woman gave birth to the baby boy at home, where her mother assisted her. The accused allegedly slit the throat of the child and then packed it in a blue bag and dumped out of the widow of their building," a police officer said.
During the probe, the police were informed that one of the women in the building was pregnant. When they inquired with the woman about her pregnancy and child, she could not give satisfactory answers.
Senior police inspector Gajanan Kabdule, of the Manpada police station said that further investigation into the matter is on.