Premier Sean Chen said at a news conference that his health condition did not allow him to fulfill his heavy duties as head of the Cabinet.
President Ma Ying-jeou's office said Ma has accepted Chen's resignation. He will be succeeded by Vice Premier Jiang Yi-hua, the office said in a statement.
The 63-year-old Chen is a prestigious financial expert. He became premier shortly after Ma was re-elected to his second term in January 2012.
His first job was a difficult, unpopular task to resolve the government's worsening fiscal problems.
The Cabinet's decision last year to raise oil and electricity prices has led to moderate inflation, which has triggered widespread public grievances. Many Taiwanese complained that their salary levels are among the worst in Asia.
Chen has also been criticized for failing to coordinate and promptly implement policy changes to deal with the impact of the global economic crisis.
Taiwan's export-driven economy has slowed amid weakening foreign demand for its technology and other goods. The island's economy grew only 1.2 percent last year. The government projects 3.5 percent growth for this year amid signs of a global recovery.
Ma's popularity has plunged below 20 percent with rising public complaints about declining living standards and Ma's perceived weak leadership.
Ma won some plaudits this week after he announced a wide-ranging reform to cut pensions for government retirees, from between 90-100 percent to 75-80 percent.
Officials say the pensions, among the best in the world, have pushed Taiwan to a fiscal crisis.