The corruption scandal was recently revealed in an investigation by Ukraine's security service (SBU), which previously made a statement that 64 officials had been informed that they were being investigated for illegally issuing disability certificates.
"Nine more people have already been convicted," the SBU said in the statement, adding that 4,106 disability certificates "had been withdrawn".
Mobilization in Ukraine is a highly debated and polarizing issue in society after a large-scale military recruitment campaign earlier this year.
"Many shameful facts about irregularities have emerged within the prosecution authorities in Ukraine," Kostin said in a statement on social media.
"I believe it is right to announce that I am resigning from the post of Prosecutor General," he added.
President Volodymyr Zelenskyj said in his daily address to Ukraine that Prosecutor Kostin had made a correct decision, and that Kostin should take "political responsibility" for the situation within the prosecution authority.
Zelenskyj also said that corruption is widespread within several authorities and not just concentrated to the prosecution authority.
There are hundreds of such cases of indefensible problems within customs, tax authorities, pension funds, and local authorities.