The Grand Depart, as the opening stage is known, is regularly held outside of France. The 2015 race started in the Dutch city of Utrecht, while the Tour got underway in Northern England in 2014.
"The state and the municipalities and regions along the expected race route have just agreed," the ministry said in a statement.
Denmark's Business and Growth Minister Troels Lund Poulsen said: "The Tour de France is one of the world's biggest sporting events, with around 3.5 billion TV viewers.
"Denmark is one of the world's leading cycling nations, and we must show that. The hosting of the Grand Depart is a unique opportunity.
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"It is positive that we, across the state, the regions and municipalities, have joined forces to attract the Grand Depart of the Tour de France to Denmark in 2018."
Poulsen said that the Scandinavian nation had done the necessary homework and would soon be contacting the race organisers.
"Later this month I will meet Tour de France race director Christian Prudhomme, where we will discuss the Grand Depart possibilities for Denmark," he said.
Bjarne Riis is the only Dane to have won the Tour De France when he triumphed in 1996, but the cycling-mad nation has previously hosted the Road World Championships in 2011 and the start of the Giro d'Italia in 2012.
(Reporting by Philip O'Connor in Stockholm; editing by Toby Davis)
