The passengers were allowed on the 20 January flight to Medina despite every seat being filled, the airline said.
Details of the flight have only emerged now because of extensive investigations by Dawn newspaper.
Staff had issued additional handwritten boarding passes, the paper reported.
Such an over-crowded flight would have caused problems in an emergency evacuation, aviation experts said, and passengers would not have had access to oxygen if it was suddenly required.
This is the first time the airline is known to have boarded excess passengers on a flight.
The flight in question went from Karachi to Medina carrying a total of 416 passengers, on a Boeing 777 with a total seating capacity of 409, including staff seats.
Dawn accuses Pakistan's  Civil Aviation Authority of "not taken punitive action against the airline or its staffers for putting the passengers' lives at risk".
The newspaper quoting airline sources accuses PIA ground traffic staff of issuing handwritten - rather than computer-generated - boarding passes to the extra passengers.
It quotes flight captain Anwer Adil  as insisting that he was not told about the extra passengers until after take-off.
"I â€¦ noticed [that] some people were those who were categorically refused jump [staff] seats by me at the check-in counter before the flight", he was quoted by Dawn as saying.
"I had already taken off and the senior purser did not inform me about extra passengers before closing the aircraft door.
"Therefore after take-off [any] immediate landing back at Karachi was not possible as it required a lot of fuel dumping which was not in the interest of the airline."
PIA spokesman Danyal Gilani told the BBC that "the matter is under investigation and appropriate action will be taken once responsibility is fixed".
When asked how long the inquiry will take, he said it was "not possible to put a time frame on it".
In December, all 48 people on board a PIA plane were killed when it crashed in the north of the country.
Pakistan International Airlines is investigating how seven extra passengers were allowed to stand in the aisles on a flight to Saudi Arabia, a spokesman told the BBC.