Odenberg has been locked in disagreement with Finance Minister Anders Borg about funding for the Scandinavian country's defense forces, SVT said.
The Defense Ministry declined to comment on the report, but said Odenberg would hold a news conference later Wednesday.
Earlier this year Borg announced plans to cut military spending by up to 4 billion kronor (EUR426 million; US$578.5 million) by 2010.
The supreme commander of the Swedish Armed Forces criticized that announcement and received support from Odenberg, creating a rift in the four-party government, which took office less than a year ago.
News agency TT said Trade Minister Sten Tolgfors would replace Odenberg as defense minister.
The discovery of the submarine has unveiled a few "inconsistencies." For example, how can one explain the fact that the sub was found where it needed to be searched for from the start?
The TurkStream, which runs along the bottom of the Black Sea from Russia's Anapa to Turkey, will consist of two lines, each with a capacity of 15.75 billion cubic meters of gas a year