Apex Council chairperson Richard Gundani told Xinhua that the teachers had heeded the call to stay away from work.
Teachers form the bulk of the civil servants.
"The situation coming from the ground is that the stay away has started. It started slow in some places because authentic information had not reached them but as soon as they got the information, the number of those going back home started to increase," said Gundani.
He said the strike, expected to include all civil servants, will run from July 5 to 7.
The cash-strapped Zimbabwe government failed to pay teachers and nurses their June salaries and deferred them to July 7 and 14 respectively. The rest of the civil servants would also get their salaries on July 14.
Gundani said the teachers' strike was aimed at "getting the message to the government that the difficult situation requires urgent intervention to ensure teachers are able to go back to work".
The government last week paid the workers an advance salary 100 U.S. dollars for transport but the workers have rejected it.
The Zimbabwe government has been failing to pay its workers on time since last year due to serious cash flow challenges. It spends about 80 percent of the national budget on salaries.
