A security review has been launched after a newspaper reporter gained access to Sandhurst military academy, where Prince Harry trains.
The Sun says its footage shows Prince Harry was at Sandhurst
The Sun said its journalist walked in the grounds of the academy for seven hours after posing as a student.
Once inside, the reporter constructed a fake bomb in his car and took grainy video footage of the prince.
Defence Secretary John Reid demanded a "quick investigation" into what he termed a "serious security breach".
"There are no excuses," Mr Reid told BBC News.
"We ought to expect a reasonable degree of security when it comes to our armed forces.
"And we ought to expect a pretty good degree of security when it comes to the Royal Family, so when you put them both together things like this shouldn't happen."
The Ministry of Defence said it was taking the breach "extremely seriously".
An MoD spokesman confirmed Sandhurst was conducting a security review.
"We will be implementing any changes we feel are necessary," he said.
The Sun said it had acted after being tipped off by a "concerned insider" worried about the state of security at the academy.
The paper's managing editor, Graham Dudman, told BBC News its actions were intended to "expose, for the public interest, gaps in security".
"What would have happened if that hadn't been the Sun that the source had called, what if he'd called somebody far more sinister?" he told BBC Radio 5 Live.
"You would have a completely different news agenda today - you wouldn't be trying to talk down the Sun on a fantastic piece of journalism, you'd be talking about something a whole lot more serious and dangerous.
"Everything about the reporter was suspect but it wasn't picked up," he added.
The newspaper said its reporter posed as a "warfare student", arranging an appointment at the military college to carry out research on the causes of the Gulf War.
Sandhurst is the army's most prestigious academy
He was waved through security and strolled into the library before wandering off, the paper said.
He later went back to his car where he constructed a fake bomb with wires, modelling clay, a battery and clock.
A policeman challenged him soon afterwards but allowed him to stay on the base, it was reported.
On its front page, the Sun printed a picture of the prince with fellow cadets, taken from video footage from their reporter.
Harry is an officer cadet at Sandhurst.
Former Sandhurst cadet and instructor Rory Clayton said the academy was designed in a university campus style to "give free movement to cadets" and was "not supposed to be a fortress".
"I'm sure security immediately around Prince Harry, as it is around all the royals, is very tight indeed," he told BBC News.
"I think the last thing the Sun's antics are going to trigger are a revelation of just how tight that security is."
In the past two years the royal family's security has been breached by a stand-up comedian dressed as a female Osama Bin Laden; a Mirror reporter posing as a footman; and a campaigner wearing a Batman outfit.
A review of royal security, last year, concluded the most likely source of "insider threat" was from the media and individuals.
It said any weaknesses which could be exploited by them could also be exploited by terrorists.