Kensington Palace has written to the media urging them not to publish pictures of Prince George taken by paparazzi photographers who are going to "extreme lengths".
A statement said the Duke and Duchess of Cambridge "are concerned about their ability to provide a childhood for Prince George and Princess Charlotte that is free from harassment and surveillance" after a series of inappropriate incidents.
It added that tactics being used by paparazzi to observe and monitor Prince George's movements "are increasingly dangerous".
Kensington Palace also said that the Duke and Duchess have "enjoyed sharing an increasing number of photos of their children and look forward to continuing to take them to more public events as they get older".
The statement made reference to a "disturbing" incident which took place last week when a photographer rented a car and hid in the boot in a bid to capture images of the young prince.
The Palace said the incident was not an isolated one, and in recent months, photographers have:
On multiple occasions used long range lenses to capture images of The Duchess playing with Prince George in a number of private parks.
Monitored the movements of Prince George and his nanny around London parks and monitored the movements of other household staff.
Photographed the children of private individuals visiting The Duke and Duchess's home.
Pursued cars leaving family homes.
Used other children to draw Prince George into view around playgrounds.
Been found hiding on private property in fields and woodland locations around The Duke and Duchess's home in Norfolk.
Obscured themselves in sand dunes on a rural beach to take photos of Prince George playing with his grandmother.
Placed locations near the Middleton family home in Berkshire under steady surveillance.
The couple's communications secretary, Jason Knauf, said: "It is of course upsetting that such tactics - reminiscent as they are of past surveillance by groups intent on doing more than capturing images - are being deployed to profit from the image of a two-year-old boy.
"In a heightened security environment such tactics are a risk to all involved. The worry is that it will not always be possible to quickly distinguish between someone taking photos and someone intending to do more immediate harm".
Kensington Palace added that the Duke and Duchess of Cambridge "have enjoyed sharing an increasing number of photos of their children and look forward to continuing to take them to more public events as they get older".
Meanwhile, Scotland Yard warned photographers that they face putting themselves in danger at a time when the national security threat level from international terrorism is severe.
In a statement, the Met Police said: "The covert actions of photographers have at times caused concerns during police protection operations when they have been considered a possible security threat."
It continued: "Photographers are potentially putting themselves at risk from armed intervention where our armed officers perceive a risk to the personal safety of their principal, the public and themselves.
"When assessing potential threats, armed officers have to make split-second decisions regarding their use of force in order to protect their principals, the public and their colleagues.
"Whilst the majority of photographers work responsibly, we would ask those that choose to use covert tactics to consider their actions in light of this potential risk."