Teachers, doctors and nurses were among who stopped work because they had not been paid in more than a month.
It comes a day ahead of a suggested national shutdown called by activists complaining about the economy and alleged government corruption.
Police used teargas and water cannons to break up protests in some areas of the capital, Harare, on Monday.
The unrest had begun when minibus drivers erected barricades in a protest against harassment and roadblocks by police demanding bribes.
Teachers, doctors and nurses have not been paid for a month, but the government has said they will get their wages by the middle of July, Reuters news agency has reported.
The scene in the country's capital, Harare, resembled a quiet Sunday afternoon, with civil servants on strike, the BBC's Brian Hungwe reports.
"We have heeded the call" by our governing council, Zimbabwe Teachers' Union president Richard Gundani said.
"Teachers and the rest of the civil servants are declaring their incapacity to go to work. Government departments were operating without some of their staff who stayed at home."
Our correspondent says unlike other government workers, the security forces were paid on time in June.
Those who were not paid were handed a $100 (Â£76) advance to help with transport and other costs.
Zimbabwe has become increasingly volatile in recent weeks as the government struggles to cope with a severe cash shortage and the effects of a drought.
Political activists, backed by the social movement called #ThisFlag, have called for a national stay-away on Wednesday "to shut down the country" in protest at the government "for allowing corruption, injustice and poverty".
On its Twitter account, #ThisFlag said it wanted "good governance and leadership" in Zimbabwe.
"Citizens. They do not have enough guns and man power to kill us all. The country has broken down. We demand an engine overhaul," said one message.
It is not clear if the national shutdown has been called for one day or indefinitely until demands are met, our reporter says.
Government workers in Zimbabwe have gone on strike over unpaid salaries because of a chronic cash shortage.