It's the second time Federal Court has been asked for an injunction to force Kent to issue an emergency protection order.
Last fall, a judge declined to force Kent's hand, ordering him instead to reconsider his refusal to make the order and supply his reasons.
Last month, Kent stuck to his guns, saying that caribou aren't in immediate danger of extinction on a national level.
While there are about 32,000 woodland caribou across the country, Alberta's herds are struggling and many scientists don't expect them to survive in the face of intense energy development.
The legal action has been filed on behalf of two environmental groups and four First Nations.