Hirohisa Fujii, 77, the former Finance Minister checked into hospital last week, suffering from fatigue and high blood pressure.
Hatoyama had told reporters Wednesday morning that he hoped Fujii would stay in his Cabinet, saying he needed his support to help pass a draft of the budget in the upcoming Diet session, set to start January 18.
His resignation was another blow to Prime Minister Yukio Hatoyama as he was struggling to enter a key budget battle in the Japanese parliament.
Japanese media said that one reason Fujii wanted to quit was because he felt he had been slighted in favour of Democratic Party Secretary-General Ichiro Ozawa in the budget wrangling.
The resignation is the first of Hatoyama's administration and could signal a fraying of the government's leadership. The government also suffers from a lack of clarity about who controls policies.
Hatoyama's approval ratings have fallen from 70 percent to 50 percent since his election four months ago.