The video was published in the daily newspaper Jutarnji List and shows Dabro sitting in the passenger seat, shooting out through the window into the darkness, singing along to loud music.
On Saturday, Dabro, who is also the Minister of Agriculture, wrote that he had submitted his resignation.
"I am aware that these circumstances create an additional burden for the government and my party", he writes.
In an initial reaction on Friday, Dabro stated that the video was filmed several years ago and that he was firing practice shots, according to the news agency Hina.
Dabro holds a leading position in a nationalist far-right party in Croatia.
