Lawyers for the Duke and Duchess of Cambridge have sent a legal warning letter to the photographers to "cease harassing" Prince George, third in line to the throne, and his nanny.
A Kensington Palace statement said they were prompted to take action after attempts to take pictures of Prince George in a central London park.
"No parent would tolerate the suspicion of someone pursuing and harassing their child and carer," it said.
The couple are not taking legal action at this stage, the BBC reported.
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The palace statement added: "There is reason to suspect that the individual may have been placing Prince George under surveillance and monitoring his daily routines for a period of time.
"The duke and duchess understand the particular public role that Prince George will one day inherit but while he is young, he must be permitted to lead as ordinary a life as possible."
Maria Teresa Turrion Borrallo was named as the prince's nanny in March when the palace appealed for her privacy to be respected.
He has also been pictured accompanying his parents on state visits and with the palace's consent at other events.
Before the royal couple married, the Middleton family raised privacy concerns about alleged harassment by press agency photographers.
In 2012, lawyers for the pair also took action against French gossip magazine Closer for publishing topless photos of the duchess.
The royal family has had a testy relationship with the British media, which reached its lowest ebb when William's mother Diana was killed in a horrific car crash in Paris in 1997 as her vehicle was being pursued by paparazzi.