The helicopters, made by Sikorsky and with mission systems integration by Lockheed Martin, will replace the country's fleet of Lynx aircraft.
The ministry said all parties of the coalition government have agreed to the ministry's choice and that a formal request for funds to buy the aircraft will be submitted to the Parliament's Finance Committee.
Nine aircraft will be purchased and be used for surveillance, fisheries inspection and search-and-rescue missions.
Denmark said it hopes to receive the helicopters over a two-year period beginning in 2016, the ministry said. The cost of the planned procurement wasn't detailed.
The MH-60R is a multi-mission maritime helicopter primarily used by the U.S. Navy. It has a maximum speed of 208 miles per hour, a range of 450 nautical miles at cruise speed and a service ceiling of 12,000 feet.