Rupert Murdoch's tabloid newspaper printed the photos, thought to have been taken on a camera phone in a hotel room, after they were originally released by US gossip website TMZ.
The paper went with the images despite warnings from lawyers on behalf of the Royal Family that it would be an invasion of Harry's privacy.
In a statement today, the Palace said that it would "not be prudent to pursue the matter further".
A Royal Family spokesperson said that the prince was "focused entirely on his deployment in Afghanistan", and so pursuing the complaint "would not be appropriate at this time and would prove to be a distraction".
''Having considered the matter now for a number of weeks, we have decided not to pursue a complaint with the PCC on behalf of Prince Harry in respect of the photos of the Prince taken in Las Vegas. We informed the PCC yesterday," the spokesperson said.
''We remain of the opinion that a hotel room is a private space where its occupants would have a reasonable expectation of privacy.
''Prince Harry is currently focused entirely on his deployment in Afghanistan, so to pursue a complaint relating to his private life would not be appropriate at this time and would prove to be a distraction.
''We have concluded that it would not be prudent to pursue the matter further, and we will have no further comment to make about the matter.''
Copyright: Rex Features Paul Grover/Rex FeaturesSt James's Palace had warned UK newspapers that running the pictures, said to have been taken while the prince played "strip billiards" at a private party with friends, would be an invasion of Harry's privacy.
However, The Sun defied the warning, and argued that there was "a clear public interest in publishing the Harry pictures, in order for the debate around them to be fully informed".
The paper claimed that Harry had "compromised his own privacy" by "frolicking in the pool before inviting strangers to his hotel room for a game of strip billiards".
Around 3,800 complaints have been submitted to the PCC about the paper's publishing of the photos, but the regulator has said that it would be "inappropriate" to investigate the situation in the absence of an official objection from the prince.