A Prince Albert lookalike had used a video contact supposedly from the ruler's own office to target the Riviera elite, the Monaco-Matin newspaper said.
The government of the millionaires' playground issued a statement confirming such hi-tech stings but without naming the prince, who boasts a fortune estimated at some two billion euros ($2.4 billion).
"For several weeks, individuals who are part of organised groups, have been stealing the identities of high-ranking personalities in the principality and trying to establish personal contact with them... notably through electronic messages, SMS or video-conferencing via a WhatsApp type of application," the statement said.
It described the targets as "leaders of society or people with responsibility" who were hit with an elaborate con.
Messages on headed notepaper from official bodies in Monaco signed apparently by the relevant people have been sent and calls can appear to come from the real numbers for the institution, the government added.
"All this is intended to obtain, under the pretext of an urgent financial need, money transfers from foreign bank accounts, particularly in Asia."
Monaco-Matin said three company bosses had recently been targeted.
It said a well-known French journalist had also been approached last September with a fake prince supposedly trying to negotiate a cash payment for the release of a local man kidnapped by an Islamist group.
The attempted con failed and police launched an investigation but could not track down the perpetrators and the con trick seems still to be going on.
Police urged people to take particular care and verify contacts from unusual sources.
Albert took over as ruler of the rocky statelet's 32,000 population after the death of his father Prince Rainier in April 2005.
Glamorous Monaco attracts high-rollers with tax breaks, the legendary Monte Carlo casino and a sunny coastal lifestyle.
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