Peter MacKay signed a contract with the shipbuilding company to review the design and specifications of the Arctic offshore patrol ships, as well as develop a plan on how they would be built.
The Arctic offshore vessels are the first expected to be built under the national shipbuilding procurement project.
"The starting gun has gone off," MacKay told a news conference at Irving's Halifax shipyard.
But Steven Staples, president of the Rideau Institute, said the federal government should be focused on replacing the navy's aging frigates and supply ships before building the Arctic offshore patrol vessels.
"These should be the priority for the naval replacement, not building these Arctic patrol vessels that are really just still on the drawing boards," Staples said in an interview from Vancouver.
"These are the wrong ships at the wrong time."
Prime Minister Stephen Harper has often said that boosting Canada's Arctic sovereignty through military presence is a priority for his government.
Steve Durrell, president of Irving Shipbuilding, said the company hopes to be ready for the design phase of the project by the end of the year.
Durrell said the goal is to start cutting steel on the patrol vessels by late 2014 or early 2015.
In October, Ottawa announced that the Irving shipyard would receive the lion's share of the national shipbuilding procurement project. Under its $25-billion deal, the yard is expected to build 21 combat vessels.
The Seaspan Marine Corp. shipyard in Vancouver will construct seven vessels under an $8-billion contract for non-combat ships.
Another $2 billion for smaller vessels is yet to be allocated to another shipyard.
Ottawa's goal in rolling out the national shipbuilding procurement program is to end the boom and bust cycle that has hampered shipbuilding in Canada in the past. The industry has struggled since the last major warship project ended in the 1990s.
The plan aims to see a steady flow of work over the next 20 to 30 years in order to sustain highly skilled jobs.