The non-binding motion, filed by the Democratic Party of Japan and two other parties in the opposition-controlled upper house of parliament, criticized Fukuda's handling of elderly healthcare insurance and blamed him for other domestic problems.
The opposition has been dogging Fukuda since he became prime minister in September in its effort to force new elections.
The motion, if approved in the upper house, will make Fukuda the first prime minister to face such a measure, Kyodo news service reported. But its non-binding clause won't result in the toppling of the Fukuda government, whose Liberal Democratic Party controls the more powerful lower house.
Supporters of the motion plan to boycott parliamentary proceedings after the censure motion passes, the report said.
However, Fukuda's ruling coalition is likely to counter it with a motion of confidence in the Cabinet, expected Thursday.
"I understand that they want to appeal to the public politically but I don't really see what kind of meaning it would have legally, or in the parliament," Chief Cabinet Secretary Nobutaka Machimura said.
The health insurance program has come under attack because critics say it places a heavier financial burden on elderly people with low incomes.