It comes as authorities investigate how two returned travellers contracted the virus while in hotel quarantine in Perth.
Mr McGowan will on Thursday ask his national cabinet colleagues to consider seeking health advice about implementing a temporary pause on arrivals from India.
He says quarantine systems are under pressure from a surge in cases overseas and particularly in India, which is dealing with almost 300,000 new daily infections.
"Just in WA, in the past month alone 40 per cent of cases in quarantine had recently been in India. In the previous month it was just 11 per cent," Mr McGowan said in a statement.
"India is facing a severe third wave, one that we haven't seen anywhere else.
"With more and more arrivals coming from India, we need to seriously look at temporarily restricting travel of people who have been in or through India."
Health experts believe a new "double mutant" strain - dubbed B.1.617 - is likely to be behind the surge in cases on the subcontinent.
WA authorities are closely monitoring infections linked back to the strain, which has also been detected in other countries.
"Our thoughts are with our friends in India at this difficult time, as well as with our Western Australian Indian community," Mr McGowan said.
"They are trying to put a stop to the third wave, however in Australia we need to do everything we can to keep this double mutant variant away."
An investigation is underway into how two returned travellers contracted the virus while in hotel quarantine.
WA Health had reported the infections as being acquired overseas, but genome sequencing has since confirmed transmission occurred at the Mercure Hotel Perth.
"The virus was transmitted in hotel quarantine at the Mercure Hotel Perth, as two sets of guests, in rooms opposite each other, had the same sequence of virus - despite arriving from different countries at different times," it said in a statement.
Other guests who stayed on the same sixth floor at the same time were previously released from the hotel after testing negative.
They will be re-tested and directed to self-isolate until cleared.
People who were in rooms immediately adjacent to the infected people will be asked to self-quarantine for 14 days.
WA's acting chief health officer has begun an investigation into how the transmission occurred.
"While similar transmission in hotels in other jurisdictions has not resulted in community transmission, the community must always remain vigilant," the department said.