The commemorative stone in Duchess Park, Motherwell, North Lanarkshire, was vandalised with graffiti including “Franco” and “vermin” as well as what are thought to be fascist symbols.
The memorial is dedicated to North Lanarkshire volunteers who went to Spain to fight against General Franco’s fascist rebellion.
A Police Scotland spokeswoman said the incident was reported to police on Saturday and inquiries were continuing.
MSPs have condemned the desecration of the memorial.
Scottish Green MSP for Central Scotland, Gillian Mackay, tweeted: “This graffiti appearing weeks before annual commemorations is particularly callous.
“The right-wing nature of it is concerning. I’ll shortly be in touch with the committee at the park to see what support they need. If anyone has information about the vandalism get in touch.”
SNP MSP for Motherwell and Wishaw, Clare Adamson, also tweeted the image, saying she is “absolutely gutted to see this on a memorial”.
Volunteers from Lanarkshire had a proud record of service in the Spanish Civil War, particularly from the Bellshill area, where a number of women joined the force to fight Franco.
North Lanarkshire Council said in a statement: “We’re very sad to learn the Spanish Civil War Memorial at the Duchess of Hamilton Park in Motherwell has been subject to an appalling act of vandalism.
“We urge anyone with any information to contact @policescotland on 101.
The rise of the Fascist right can be seen in many guises in Scotland and across Europe, this is a hallmark of their cowardly work.