The protest involves affiliates of the Trade Union Congress of Swaziland (TUCOSWA) which has a membership of over 25,000 unionised civil servants, 11,000 teachers and more than 4,000 nurses.
"Due to the uncertainty of the safety and protection of children during the proposed industrial action scheduled for 18, 19 and 20 September by TUCOSWA, the Ministry of Education and Training advises that classes be suspended to ensure that their children are kept at home during these dates," the government said in a statement.
It said classes are expected to resume on 24 September.
The protest is a result of failed cost of living adjustment negotiations, which saw the government failing to give civil servants a salary hike for the second year in a row.
The strike comes days after nurses engaged in a strike last week to protest a shortage of medication and working tools at almost all the country's public health facilities.