Officials say the falcons were brought from Qatar by a member of its royal family without proper documentation.
They say another 22 birds have been handed back to the Qataris.
Members of Gulf royal families routinely bring in falcons for hunting birds and other animals in Pakistan, with government sanction.
The Qatari embassy was given several days to produce paperwork relating to the import of the birds – but customs officials say documents for only 22 could be furnished.
“But the 52 falcons were later released into the wild in Kirthar National Park,” Mr Baloch said.
Located just outside Karachi, the park has a variety of wildlife within its 250,000 hectares.
Although locals are prohibited from hunting the birds, it is thought members of Gulf royal families are given special permission to do so.
Conservation groups say such licences are illegal and unprecedented elsewhere in the world.
Hundreds of thousands of Pakistanis are employed in various industries in the Gulf kingdoms, which also provide bailout loans and cheap oil to Pakistan’s perpetually beleaguered economy.
For this reason, many see the licences as being in Pakistan’s national interest, correspondents say