"Any such act should be condemned by us all and we must protect our fellow citizens," he told reporters.
He said he had information that glass was smashed on the premises and that "some kind of explosive device" was thrown inside.
"I realise that the cause is probably the situation in Vukovar, but we are in Split, (the Serb national minority) are our fellow citizens who have their premises, given to them by the city, as to many other national minorities and associations."
The mayor said this act of "vandalism and hooliganism" was committed by fools.
Split police said they arrested two men in connection with the incident.