The Minister for Justice Mr McDowell is under pressure to explain how confidential department documents ended up in an illegal dump in Co Tyrone.
Among the documents was a briefing paper from the Department of Justice concerning a proposed meeting with the Department of Finance.
The discovery at Eskra comes just nine days after it emerged that the Department of the Environment in Northern Ireland had set up a special team to combat rising incidences of illegal dumping from south of the border.
Officials have uncovered up to two illegal sites every week containing tens of thousands of tonnes of waste from across the Republic.
Labour Party Justice spokesperson, Mr Joe Costello, said the discovery was "highly embarrassing" and must be explained by Mr McDowell.
Sinn Féin's Mr Arthur Morgan said: "For these documents to come in the form of rubbish from the Minister for Justice's office is extraordinary."
Both men expressed concern about the environmental implications of the find.
A Department of Justice spokesman said the matter was of "great concern" and is being investigated by the gardaí.
Additional reporting PA