It received a report of a vessel in difficulty near Lossiemouth in Moray at around 7.40am on Monday.
The Coastguard has now reported the matter to Police Scotland and officers are working with the organisation and the RNLI as part of their investigation.
Sergeant Mark Bayliss said: "We are liaising with the Coastguard and RNLI following a call made this morning reporting a vessel in difficulty.
"Any reports of distress to the emergency services will be taken seriously and it is disappointing that individuals abuse this response which takes up valuable resources.
"Our inquiries are at an early stage and anyone who may have information is asked to contact Police Scotland on 101 quoting incident 721 of 29 July or if you wish to remain anonymous, you can contact the independent charity Crimestoppers on 0800 555 111."
An RNLI spokeswoman said: "Our volunteer crews will always respond, when tasked, to reports of somebody in difficulty in the water.
"However, hoax calls divert life-saving resources away from those who could be in real danger.
"Last week, due to the heat wave, our volunteers in the north-east of Scotland were called upon many times to respond to potentially life-threatening situations.
"Had they been diverted by a hoax call then they would not have been available to respond to those in real need."
She added: "As a charity run predominantly by volunteers we rely on not only public donations to fund our life-saving service but also the goodwill of our volunteers and their employers.
"We hope that anybody with information around this hoax will get in touch with Police Scotland or Crimestoppers."