The gang swapped newborn babies with the bodies of dead infants in hospitals and maternity homes, and told their parents the child had died, police told the BBC.
The babies were then sold to childless couples for between 70,000-300,000 rupees (£500-2,200; $650-$2,850).
Pakistan has seen several high-profile cases of baby abductions recently.
Police told the BBC they had received a number of complaints about stolen babies.
Some women who had given birth to healthy babies said they were told within hours that their child had died