Mr. McGowan confirmed that his office in Rockingham was closed after employees were subjected to threats.
“There have been death threats and there have been threats to rape my staff,” McGowan told reporters.
“It is disgusting and disgraceful and they should stop because it will not make the government change its policy.”
The threat of rape was made in person to an employee and is now being investigated by the police.
The government has come under fire from anti-vaxxers after implementing a vaccine mandate for the majority of the workforce.
Viceliberal leader Libby Mettam also condemned the “cruel” behavior and expressed his sympathy for the premiere.
In Parliament on Tuesday, Mr McGowan branded some anti-waxers as “disturbed”.
“What we have seen both in WA and in Victoria has been insane and crazy, some of the behavior is insane, they are insane, they are crazy behavior,” he said.
“This is not the Australian way.”
Mr. McGowan urged all eligible Western Australians to step up to the jab.
“We have to stand together in this time of trouble and strife.
“My advice to everyone is to go and get vaccinated.”
More than 70.5 per cent of Western Australians aged 16 and over have received two doses of vaccine.