Bozize was expected to name a new prime minister in the coming days to form a new administration.
The poor former French colony has experienced several coups and attempted coups in the past decade.
Western diplomats in Bangui said the strike, coupled with the government's resignation, could trigger a deeper political crisis.
The Central African Republic's main trade unions launched a general strike on January 2 to demand that the government pay seven months of arrears in salaries to civil servants and teachers.
The stoppage has provoked demonstrations in the streets of the capital, Bangui, by students angry about not being able to attend classes.
The government says it does not have the funds to pay the salary arrears, and a meeting between Bozize and union leaders on Thursday failed to reach a settlement.
Bozize seized power in 2003 but then won elections two years later with support from the unions now staging the stoppage.
The Central African Republic is already facing a humanitarian emergency in its northwest and northeast, where raids by several armed groups and counter-attacks by government soldiers have driven nearly 300,000 people from their homes since 2006.
EU peacekeepers are due to arrive in the country in February.
The peacekeepers, to be deployed into the country's northeast, are part of a larger EU force that has a UN mandate to protect civilians in eastern Chad from violence spilling over from Sudan's Darfur region.