The Tonga women's team left the championship in Fiji under instruction from the Fijian Government in consultation with the World Health Organisation.
Oceania Rugby said the decision was made after the team was forced into quarantine for 18 days - which would run through the tournament.
One of Tonga's players who arrived in Fiji was suspected of having measles.
The tournament was due to produce a directly qualified team for the World Cup and a team to participate in the repechage tournament.
World Rugby said recognising the level of investment made by teams to participate in the championship, and to provide Tonga with an opportunity to qualify for the World Cup, a revised qualification process had been agreed.
The winner of the championship will still qualify directly for the World Cup but early next year, Tonga will travel to the country which comes third in the championship for a play-off.
The winner of that match will play against the second-placed team to decide who will compete in the repechage tournament.
Rugby World Cup will cover the costs of both additional test matches.
Both Australia and New Zealand have already secured qualification for Rugby World Cup 2021 as a result of finishing in the top seven placed teams at Rugby World Cup 2017 in Ireland.
Rugby World Cup 2021 will be hosted in New Zealand.
Meanwhile, the New Zealand Development XV and Fiji came out victors in their games against Australia A and Samoa's Manusina XV respectively in round two on Friday.
Round three of the championship kicks off on Tuesday in Fiji with the New Zealand Development XV taking on the Papua New Guinea Palais and Australia A meeting Samoa's Manusina XV.