Daithí McKay said DFP has not co-operated with the committee regarding the inquiry since July.
The committee is investigating the sale of property loans by the National Assets Management Agency (Nama).
The inquiry was set up after claims a politician was set to profit.
The claim was initially made in the Irish Parliament in July, where an independent member, Mick Wallace, alleged a politician in Northern Ireland was in line to gain from the deal, via a £7m bank account in the Isle of Man.
Politicians, Nama officials, businessmen and companies involved in the deal have all denied any wrongdoing.
Nama: The key figures and background you need to know
Timeline of Nama's NI property deal
The inquiry chairman told MLAs that the DFP has not responded to the committee's requests for information, nor has its permanent secretary returned to appear before its members to answer questions.
"I think its position, in regard to the Nama review, is totally untenable," Mr McKay said.
"The department is remarkably shy about issuing papers. If the department has nothing to hide they need to bring these papers forward," the Sinn Féin MLA added.
"The public will come to their own conclusions, whether they are right or wrong, the more the department continue to pull down the shutters in regard to our review."
The Stormont inquiry is one of five international investigations into the loan sale, known as Project Eagle.
The relationship between Stormont's Department of Finance (DFP) and its scrutiny committee is at "rock bottom" in relation to the Nama inquiry, the committee's chairman has said.