Shop stewards from the GMB, Unite and Community unions recommended that no action be taken after they received the results of the ballot of 5000 workers.
They decided to defer any action for 28 days so that discussions could take place with the workforce about the future of the factories.
Some 2,400 workers were facing redundancy but this threat appears to have been lifted for the time being after Mr Hain promised a moratorium and a review.
In addition, government departments and local councils are to be encouraged to place new orders with Remploy factories to keep them open.
A new £150m contract for nurses and military uniforms is the most likely order to get the go-ahead.
The GMB union yesterday decided that the government's agreement to defer any action and remove the power of the management at Remploy to close factories was enough to call off a strike.
The government is to look at £50m savings from management in the running of the factories, but this will not affect the jobs of disabled workers.
Remploy - whose factories employ thousands of disabled people - was set up in 1946 to provide work for disabled ex-servicemen. It receives an annual grant from the government to fund training, development and the finding of employment for disabled people.
