The prank involves people dressing up as clowns to deliberately scare or intimidate members of the public.
Police Scotland said it had received a "few sporadic reports of individuals dressed as clowns" in some areas in Scotland.
The reports did not specifically involve threats or violence.
But police said anyone "seeking to cause distress and potential harm to anyone" should be aware that action would be taken.
The craze appears to have been inspired by clown-related pranks in the US and has seen a string of copycat incidents across the UK recently.
Last week a hoaxer admitted a "sighting" in Glasgow was faked.
A Facebook page called "Killer Clowns in and around Glasgow" said a clown had been spotted underneath a bridge.
The post was shared more than 1,000 times before the poster admitted the picture had been taken elsewhere.
In a statement, Supt David Duncan, from Police Scotland, said: "We have had a few sporadic reports of individuals dressed as clowns in some areas in Scotland.
"It is assessed that there is a current trend of similar incidents on social media, many of which have been confirmed as hoaxes and emanate from overseas.
"The reports which have been made to local police officers are being investigated and do not specifically involve threats or violence.
"However, any person seeking to cause distress and potential harm to anyone should be aware that police will take action.
"If anyone has any concerns they should report the matter to police."
Police in Scotland have warned that action may be taken against people who take part in the so-called "killer clown" craze.