Hamas, which has controlled the Gaza Strip since 2007, has been trying combat vaccine hesitancy in the Israeli-blockaded territory, home to some two million Palestinians.
Gaza's health ministry has said it had received 768,000 vaccine doses, but only 140,000 residents have been fully inoculated.
"Legal measures must be taken against those employees who do not follow the instructions regarding vaccination," said Salama Maruf, the head of Hamas's media office.
A similar measure for unvaccinated civil servants has been in place for several weeks in the occupied West Bank, a separate territory controlled by the Palestinian Authority.
Palestinian prime minister Mohammed Shtayyeh has said that "most" new infections in the West Bank are among the unvaccinated.
In the West Bank, under Israeli military occupation since 1967, more than 234,000 Covid-19 cases have been recorded and nearly 2,700 people have died from the virus.
More than 596,000 have been fully inoculated with two jabs against coronavirus in the territory, home to some 2.3 million Palestinians, according to the PA.
In Gaza, some 168,000 covid cases have been recorded, with 1,375 deaths.