GMB and Unite members at Chesterfield, Leeds, Pontefract and Worksop began their protest at 6am this morning.
Employees across the country have already taken action, including two 24-hour strikes last week.
The workers are picketing in protest at the government’s decision to close 36 of its sites.
The closure will see 1,752 workers being made compulsory redundant, 1,518 of whom are disabled.
Since Remploy was established in 1946 the company has been run for the benefit of disabled people but is managed by non-disabled people.
Leeds Central MP Hilary Benn has called the closure decision a “bitter blow” for its workers.