In a resignation letter posted on Facebook, Dabro, who was also Minister of Agriculture, Forestry and Fisheries, said he did not want to distract the government.
He said he had been subjected to “significant pressure and threats” over plans to reform the agency.
The footage was released earlier this week.
The Good Party is part of a coalition government with the center-right Croatian Democratic Union (HDZ) party of Prime Minister Andrej Plenkovic.
Last November, Health Minister Willy Bros was fired ahead of a corruption investigation.
Zoran Milanovic was on Monday re-elected president for a second termreceiving almost three-quarters of the votes, ahead of his opponent Dragan Primorac, who was supported by the CDU party.
After the result, Plenkovic said that “Milanovic does not offer anything” and refused to congratulate him. Presidents in Croatia play a mostly ceremonial role.