Munich, which hosted the 1972 summer Games, is up against the French city of Annecy and Pyeongchang in South Korea.
The IOC is meeting in the South African city of Durban and will vote for the winner next Wednesday, July 6.
Merkel, who will be in Durban prior to the vote to press Munich's claims, said in her letter, which was addressed to the 100 delegates, that the Olympic bid was a "national affair" for the Germans "of significant importance."
Merkel, who will be accompanied by the German president Christian Wulff and Interior Minister Hans-Peter Friedrich, stressed that the different levels of government and shades of politics were united in backing Munich's bid.
"We want to invite the world to be our guest," she said at the end of the letter.
French Prime Minister Francois Fillon has also announced that he will be heading to Durban for the vote, accompanied by Sports Minister Chantal Jouanno.
South Korean President Lee Myung-bak will also be there, promoting the hopes of Pyeongchang.
Munich has looked like an increasingly likely candidate for the games in recent months as the International Olympic Committee has rated the city nearly as highly as its South Korean competitor.
Leaders of the bid have also staved off an anti-Olympics campaign and a dispute with landowners over property.