Mr Abhisit, who has faced down two such votes since 2009, was named along with nine other ruling coalition ministers in the motion filed by Puea Thai legislators.
The opposition has little chance of winning as it lacks a majority in the lower house, but the debate is expected to serve as a start to campaigning for an election likely to be called in the first half of the year.
Thailand is deeply divided after more than 90 people died in clashes between the army and demonstrators during rallies by the anti-government "Red Shirts" in April and May last year, its worst political violence in decades.
Mr Abhisit told reporters that he expects the motion to be heard next week.
"I had already thought they would raise the crackdown issue to arouse opposition supporters," he said.
Puea Thai spokesman Pormpong Nopparit said the government had "mismanaged, corrupted and failed" in its handling of the country's problems.
"We have new information that the government was wrong in ordering its forces to crack down on the Red Shirts," he said.
Other ministers named in the no-confidence motion include Deputy Prime Minister Suthep Thaugsuban, Foreign Minister Kasit Piromya, Finance Minister Korn Chatikavanij and Commerce Minister Pontiva Nakasai.
Suthep, who is responsible for national security, is also accused of abusing authority over his part in overseeing the government response during the unrest.
"I am not complacent and the government is confident that all ministers who face a grilling can defend themselves against the allegations," he told reporters.
The Reds have held a number of large street protests in the capital in recent weeks as the first anniversary of the start of their rally approaches.
The mainly rural, working class Reds are broadly loyal to fugitive former premier Thaksin Shinawatra, who was ousted in a military coup in 2006 and lives overseas to avoid a jail sentence for corruption imposed in absentia.
They view the government as undemocratic because it came to power in 2008 in a Parliamentary vote after a court ruling threw out the previous administration.