Around 3,800 people have submitted complaints to the PCC that the paper's publishing of the photos, taken while the prince was on holiday in Las Vegas, was a breach of his privacy.
The Sun argued that as the photos had been first published by US gossip website TMZ and widely distributed on the internet, its readers had a right to see them.
The Rupert Murdoch-owned paper also said that there was a clear public interest as Harry is third in line for the throne.
In a statement yesterday (September 6), the commission said that it is continuing dialogue with Prince Harry's representatives, but has not yet received a formal complaint from the Royal Family.
It therefore said that in the absence of a complaint, it would be "inappropriate" to launch an investigation, as without consent that would "have the potential itself to pose an intrusion".
"The Commission is grateful to the many members of the public who have contacted it to express concerns about The Sun's coverage but has concluded that it would be inappropriate for it to open an investigation at this time," said the PCC in its statement.
Copyright: Rex Features Paul Grover/Rex FeaturesPrior to The Sun's publication of the nude photos, the Palace sent a note to newspaper editors warning them against using the images on the ground that it would be an invasion of the prince's privacy.
The Guardian's Roy Greenslade notes that the Royal Family now faces a dilemma over whether to make a formal complaint to the PCC.
He commented that, if the Palace resists the action, then it will appear as though The Sun has 'got away with it', meaning other newspapers will be "desperate to publish" next time such an opportunity arises.
However, proceeding with a complaint runs the risk of it not being upheld, meaning The Sun will get justification for its argument that there was a public interest, and that this is an issue of freedom of the press.
"There would undoubtedly be a split in the newspaper ranks too, between those who view publication as meretricious and those who believe it to have been warranted," notes Greenslade.
"Then, of course, there are the 3,800 members of the public who took the trouble to complain to the PCC. What faith will they have in press self-regulation should they be knocked back?"
He adds: "In truth, and this is a sobering thought as the Leveson Inquiry ponders the future form of press regulation, Murdoch looks to have won this battle already."