Loose forward Cane was given a red card for a high tackle in the 12-11 defeat to South Africa in the decider in France, leaving the All Blacks with 14 men for most of the game.
He will take up a sabbatical option in his New Zealand contract to join the Japanese League One side Suntory for the 2023/24 season and will miss the Waikato Chiefs' 2024 Super Rugby campaign, New Zealand Rugby said.
However, Cane will return to New Zealand next June to be available for selection for the international season.
"It wasn’t an easy decision to skip a season with the Chiefs, but I know the team is in a great place and has an incredible group of leaders in the squad and the coaching group to have a successful 2024," said 95-test Cane in a statement.
"And I’m really pleased to be able to return in time to put my best foot forward for selection in the All Blacks."
Cane, whose national contract runs through to the end of 2025, returned home to New Zealand this week after becoming the first player in World Cup history to be sent off in the final.
Cane said he had taken some solace from his mum's advice about not beating himself up about the red card but admitted it would take a while to get over it.
"I think it’s something I’m going to have live with forever, unfortunately. It’s going to hurt for a while."
