The Public Order (Scotland) Act 2021 came into force on 1 April.
This creates a new crime of stirring up hatred relating to age, disability, religion, sexual orientation, transgender identity or being intersex.
Critics claimed the legislation could harm free speech and senior police officers warned it could spark a flood of complaints about online posts.
But the Scottish government insisted that the law provided protection from hate and prejudice without stifling individual expression.
The figures released by Police Scotland cover the period from 1 to 7 April.
A spokesperson for the force said it showed a “substantial increase in the number of online hate reports being received”.
“This significant demand continues to be managed within our contact centres and so far the impact on frontline policing – our ability to answer calls and respond to those who need our help in communities across Scotland – has been minimal.
“All complaints received are reviewed by officers, supported by dedicated hate crime advisers, and dealt with appropriately, whether that is being progressed for further assessment, or closed as they do not meet the criteria under the legislation.”
