Speaking at a press conference on Wednesday afternoon, he repeatedly stated his opposition to the fact that the government had announced cuts in defence spending without first analyzing Sweden's military requirements.
"[The Swedish's military's] finances have been disconnected from its purpose," he told a resignation press conference.
"You can't just take away lots of defence procurement spending without it having operative effects," he said.
The cuts, he said, would damage Sweden's capacity to take part in international operations and would make it impossible for Sweden "to belong to the EU's core in defence matters."
He indicated that his decision to resign was a matter of conscience:
"I want to be able to face myself in the mirror and look our military personnel in the eye."
Odenberg said he did not have any objections to other aspects of government policy and added that he was resigning "entirely without bitterness."
Odenberg said he had also written to the speaker of Sweden's parliament, Per Westerberg, and asked to resign his seat. He did not reveal plans for the future, although said that he "plans to lose the 30 kilos I have gained since being elected to parliament."
Odenberg's resignation will be a shock to Sweden's political establishment, but the rift between him and Finance Minister Anders Borg has been apparent since early summer. Borg detailed plans in early July for an annual four billion kronor cut in the Swedish defence budget.
The finance minister said that defence minister Mikael Odenberg was on board - though Odenberg said at the time that was a "misunderstanding".
Borg argued that by 2010 the military should cut its spending by four billion kronor, or ten percent of the total budget. The cuts would primarily come from new equipment purchases.
The head of Sweden's armed forces, Supreme Commander Håkan Syrén has announced that he will hold a press conference later on Wednesday.
Commenting immediately after Anders Borg's statement in July, Syrén warned against hasty decisions being taken.
"In the end it is our politicians' role to decide the job of the military and future defence budgets, but I am seeking an unconditional discussion which starts with the operations which today's and tomorrow's Swedish military has been assigned. Most of all we should avoid drawing conclusions too hastily and too early. Not least when it comes to the finances," wrote Syrén.
He concluded his newsletter with an appeal to Odenberg.
"I understand that my view in that respect is completely in line with the defence minister's position," wrote the Supreme Commander.
Mikael Odenberg, born in 1953, has been a long-serving member of the Moderate Party. He was named Defence Minister after the coalition Alliance's election victory last September.
He began his political career as a county councillor in Stockholm in 1976 and has been a member of the Swedish parliament since 1991.
Odenberg lives in Stockholm and is married with four children.
The new defence minister has not yet been announced, although some newspapers are speculating that Trade Minister Sten Tolgfors will succeed Odenberg.
Odenberg is the third minister to resign from Fredrik Reinfeldt's cabinet. Maria Borelius resigned as trade minister after only eight days in the job. She was forced to quit after questions were raised over her tax affairs. Culture Minister Cecilia Stegö Chilò resigned two days later after admitting she had not paid her television licence fee for sixteen years.