He suffered a knee injury during his team's loss to England in a warm-up match on Monday morning (NZT), the Welsh Rugby Union (WRU) said.
New Zealand-born Anscombe (28) suffered an anterior cruciate ligament (ACL) injury in the first half and tried to play through the pain before leaving the field.
"Gareth Anscombe is out of Rugby World Cup contention after sustaining an anterior cruciate ligament injury in the match against England yesterday," the WRU said in a statement.
"His prognosis and management will be determined following further specialist reviews. The Wales squad and management would like to wish Gareth the very best with his recovery."
Anscombe had established himself as first-choice Wales first five this year. Coach Warren Gatland will name his 31-man World Cup squad in early September with Dan Biggar, Jarrod Evans and Rhys Patchell in contention for the number 10 jersey.
Wales play England again in another warm-up match in Cardiff this weekend, before facing Ireland at home and away.
They begin their World Cup Pool D campaign on September 23 against Georgia in Toyota City.