Police are treating a “White Lives Matter” slogan, which was etched into a park hillside, as a hate crime.
The message is believed to have been put in Miners Welfare Park in Bedworth at about 05:10 BST on Friday.
Warwickshire Police said it was being treated as racially-aggravated criminal damage and said officers would be increasing patrols in the area.
“This appears to be a clear attempt to stir community tensions and it will not be tolerated,” Supt Daf Goddard said.
Warwickshire Police said it was aware of footage appearing to show someone in clothing “resembling a Ku Klux Klan outfit”.
The footage on social media appeared to be at the same site, the force said.
Nuneaton and Bedworth Borough Council said a “substance used to the kill the grass” was used to create the message and the area had now been ploughed over and re-seeded.
Ian Lloyd, portfolio holder for arts and leisure, said: “This is unacceptable, disgraceful mindless vandalism which will place further costs on the borough council, yet again diverting valuable resources away from the other grounds maintenance work in trying to keep our parks and open spaces clean and tidy for all to enjoy.
“Such incidents incite racial hatred and are a matter for the police to investigate. Let me make it clear, there is no room for any racist behaviour in our borough.”
Thousands of people have marched in the UK as part of Black Lives Matter demonstrations following the death of George Floyd in Minneapolis last month.