"Translated into human language it is the distribution of money to the projects of ... lawmakers," he wrote. "This - political corruption - is known by people as 'buckwheat'".
"Buckwheat" refers to the practice of bribing voters with food or by other means during an election campaign. Ukraine holds presidential and parliamentary elections in 2019.
Danylyuk, who is Kiev's point man in the international aid negotiations, has previously said he had no plans to resign.
The finance minister has also accused Groysman of blocking his attempts to reform the tax service.
Groysman said Danylyuk's actions may have hurt Ukraine's negotiations with the European Union, from which it is also seeking more economic aid.
"The dissemination of distorted information among our international partners on the eve of important negotiations with the EU could jeopardise their results," Groysman wrote on Facebook.