The Hungarian news site 444.hu reported Thursday that a reader had spotted the warrant on the local police wanted list.
Gorka, who holds Hungarian, US and British citizenships, spent eight months working as a national security advisor to Trump between January and August 2017.
Still visible on the police.hu website Friday, the warrant dates from September 17, 2016, and states that Gorka is wanted for suspected "abuse of firearms or ammunition".
A police spokesperson told AFP in an email Friday that he was unable to provide further details on the alleged crime that triggered the warrant.
News site 444.hu said it believed the warrant may refer to an incident in 2009, but Gorka dismissed the report on Twitter.
"I moved to America in 2008. (LEGALLY!)" Gorka tweeted.
"More FAKE NEWS!" he told the British daily Guardian online Thursday.
A former editor at the right-wing news website Breitbart, Gorka gave several fiery television interviews in defence of Trump.
He now works as a security pundit for the US television channel Fox News.
While in the White House Gorka also met Hungarian Foreign Minister Peter Szijjarto in March last year.
The Hungarian foreign ministry told AFP on Friday that Szijjarto "was not aware of the arrest warrant".
"Preparing for a discussion with a high ranking White House official doesn't mean checking police.hu," it added.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)