Saturday's Pool C decider between England and France in Yokohama as well as the Pool B fixture between New Zealand and Italy in the City of Toyota have been called off.
In a statement, World Rugby and the Japan Rugby 2019 Organising Committee said: "Based on the latest detailed information from the tournament's independent weather experts, Hagibis is predicted to be the biggest typhoon of the 2019 season and is highly likely to cause considerable disruption in the Tokyo, Yokohama and City of Toyota areas throughout Saturday, including likely public transport shutdown or disruption.
"As a result, World Rugby and the Japan Rugby 2019 Organising Committee have taken the difficult, but right decision to cancel matches in the affected areas on safety grounds.
"The impacted teams have been informed and are understanding. For matches that do not go ahead as scheduled, two points will be awarded to each team in line with tournament rules.
"It is an exceptional, complex and rapidly evolving situation and team and public safety is the number one priority. This has been central in all decision-making in partnership with the tournament's weather information experts, host cities, venues and teams."
Based on the latest detailed weather information, the following update is provided: Friday, October 11: Pool D match between Australia and Georgia in Shizuoka at 19:15 JST to be played as scheduled.
Saturday, October 12: Pool A match between Ireland and Samoa in Fukuoka at 19:45 JST to be played as scheduled; Pool B match between New Zealand and Italy to be cancelled; Pool C match between England and France to be cancelled.
World Rugby and the Japan Rugby 2019 Organising Committee went on to explain that it was not an easy decision to call off the matches and said they were trying to ensure that Sunday's fixture will go ahead as scheduled.
"The decision to cancel matches has not been taken lightly and has been made in the best interests of public, team, tournament personnel and volunteer safety, based on expert advice and detailed weather information," its statement read.
"While we have extensively explored all options, public and team safety was our utmost priority as well as ensuring a consistent, fair and equitable outcome for all teams. All fans with tickets for a cancelled match will receive a full refund for the face value of their match tickets.
"Every effort is being made to ensure Sunday's matches will be played as scheduled. A thorough assessment of venues will take place after the typhoon has passed before a final decision is made on Sunday morning.
"Based on the advice of government authorities and experts, World Rugby and the Japan Rugby 2019 Organising Committee are advising fans in the Tokyo, Yokohama and City of Toyota areas to stay indoors on Saturday, not to travel and to keep monitoring the official Rugby World Cup 2019 digital and social channels, including the RWC 2019 Fan Information Twitter handle @Japan2019_ENG for regular updates."
World Rugby Chief Operating Officer and Tournament Director Alan Gilpin said when addressing the media: "This is a complex and dynamic situation which we have been monitoring extremely closely with the assistance of our weather information experts. We are now in a position to accurately predict the likely impact of Typhoon Hagibis on Rugby World Cup fixtures this weekend.
"While making every possible effort to put in place a contingency plan that would enable all of Saturday's matches to be played, it would be grossly irresponsible to leave teams, fans, volunteers and other tournament personnel exposed during what is predicted to be a severe typhoon.
"As a result, we have taken the decision to cancel some matches in order to ensure the safety of all involved. It is the right thing to do, and comes with the support of all stakeholders, including the teams.
"We fully appreciate that England, France, New Zealand and Italy fans will be disappointed, but we trust they will appreciate that their safety must come first. They will be entitled to a full refund on their match tickets.
"Our message for all fans in Japan for Rugby World Cup is to heed all official advice, stay indoors throughout Saturday and do not attempt to travel on the day."