The bodies were found from the dump near a petrol pump in the Tando Allah Yar district and police suspect that the babies were abandoned by the same person.
"It is a serious crime to dump newborn babies in this manner and under the Pakistani laws carries a jail sentence of seven years for those involved in this injustice," District Police Officer Muhammad Khaqan said.
He said the babies were discovered by a local resident who had gone to throw garbage.
"We have shifted the babies to the Civil Hospital and are investigating the matter," he added.
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Faisal Edhi of the Edhi trust, a non-profit social welfare organisation, said that in Pakistan poverty often forces parents to dump newborn babies instead of bringing them to proper orphan or care homes.
"Even couples afraid to face society in case of illicit births follow the same practice and it is really disturbing. We have run a campaign saying if any parent can't take care of his newborn he should bring it to us not dump it in this manner," Edhi said.