Mr McGowan confirmed his Rockingham office was shut after staffers became the subject of threats.
“There’s been death threats and there’s been threats to rape my staff,” Mr McGowan told reporters.
“It’s disgusting and disgraceful and they should stop because it’s not going to make the government change its policy.”
The rape threat was made in person to a staffer and is now being investigated by police.
The government has come under fire from anti-vaxxers after it implemented a vaccine mandate for the majority of the work force.
Deputy Liberal Leader Libby Mettam also condemned the “atrocious” behaviour and expressed her sympathy for the premier.
In parliament on Tuesday, Mr McGowan labelled some anti-vaxxers as “deranged”.
“What we’ve seen both in WA and in Victoria has been deranged and crazy, some of the behaviours are deranged, they’re lunatic, they’re crazy behaviours,” he said.
“This is not the Australian way.”
Mr McGowan urged all eligible Western Australians to come forward for the jab.
“We need to join together at this time of trouble and strife.
“My advice to everyone is to please go and get vaccinated.”
More than 70.5 per cent of Western Australians aged 16 and over have received two vaccine doses.