Enterprise minister Arlene Foster claimed that the film, titled Gaslands, was "one-sided" and the Co-op was irresponsible for sponsoring its screening in Belfast in March.
But the chain said that it did not "endorse" the film, but rather saw it as the "starting point for an informed debate" on the issue.
Hydraulic fracking is considered by some people as a way to unlock substantial gas deposits, such as a recent discovery in County Fermanagh in Northern Ireland.
But critics have said that it can pollute water and even cause minor earthquakes.
In a letter sent to Co-op in Northern Ireland, seen by the BBC, Foster questioned the company's support for the 'sensationalist' film.
"The strapline on your corporate website claims in large bold characters, 'We're taking ethics to the next level'," she wrote.
"I find this claim hard to reconcile with your demonstrable support for a film which presents a wholly one-sided and partial approach to the debate about hydraulic fracturing.
"Perhaps you might feel that your apparent endorsement of the screening of the film Gaslands is misplaced."
She added: "I firmly believe that Northern Ireland needs to explore the potential shale gas offers."
In response, the Co-op Group - which has almost 5,000 stores and a turnover of £13bn - defended its decision to sponsor the Belfast screen of Gaslands, along with several others across the UK.
"The Co-operative is campaigning for a moratorium on the exploration of shale gas, at least until all the risks and impacts are properly identified and addressed," said Co-op regional secretary Gerard Hill.
"The event comprises a screening of Gaslands followed by an open discussion on what shale gas development might mean for Northern Ireland.
"We do not 'endorse' Gaslands but view it as the starting point for an informed debate."
The Co-op also noted that Foster had been invited to attend a screening of Gaslands, but had declined.