The World Health Organization has declared Omicron a "variant of concern" after cases were detected in Europe, Asia and the Middle East.
"With little known about the variant, it is important we act with an abundance of caution in dealing with potential spread into WA from overseas travellers arriving in other states," Mr McGowan said.
Eight COVID-19 cases have been recorded in South Australia since it opened its borders on 23 November, although no evidence of community spread of the virus has been established.
The changes mean WA is only allowing quarantine-free travel from Tasmania and Queensland. A hard border remains in place for the other state and territories.
Mr McGowan said there was concern about the potential of the virus - including potentially the Omicron variant - to spread into WA from interstate as Australian jurisdictions relax border and hotel quarantine requirements.
"The prospect is that Omicron variant could get into Adelaide in South Australia. So it's a highly precautionary measure.
No cases of the new Omicron variant have been recorded in Australia, although cases have been identified in Hong Kong, Botswana, Belgium and Israel.
"With the Omicron variant now around the world, the chances are it will come into Sydney, Melbourne. New South Wales no longer has a hotel quarantine system at all. So it's a big risk over there," Mr McGowan said.
"That's why we have a very cautious approach because we don't have the virus here."
Mr McGowan acknowledged the changes will affect family reunions between the states over the Christmas and New Year festive season.
"I realise that it will be disruptive and also inconvenient for some families."
The federal government on Saturday announced travel restrictions for arrivals from nine southern African nations: South Africa, Namibia, Zimbabwe, Botswana, Lesotho, Eswatini, the Seychelles, Malawi, and Mozambique for two weeks.
Mr McGowan said he welcomed the precautionary steps.
"So I think what the Commonwealth has done today is vindicate the approach Western Australia has taken throughout the course of the pandemic," he said.
"That shows the borders are effective or does make a difference. if you stop the flow of people coming in, you virtually - as best you can - eliminate the virus getting here."
Mr McGowan said the plan remained the same to name a date for border reopening in early December, but that the Omicron variant will be closely observed.
"We will be closely monitoring the (Omicron) variant. This has been a long hard road. We have seen various variants along the way. We will have to see what happens with this one."