In a statement, the Blues said Barrett, who signed a four-year deal with New Zealand Rugby and the Blues last year, will miss next year's Super Rugby season and play for the Suntory Sungoliath club based in Tokyo, before returning to New Zealand for the 2021 global season.
Under the deal, Barrett will miss Super Rugby in 2021 but play for the All Blacks in late 2021 before remaining in New Zealand up until the 2023 World Cup.
Barrett, 29, signed a four-year deal with New Zealand Rugby (NZR) and the Blues in 2019, but will head to Japan in 2021 before returning for the worldwide season.
Japan has become a hotbed for top internationals in recent years with Top League sides flush with funds.
Suntory's coach is New Zealander Milton Haig while England coach Eddie Jones acts as a consultant for the club. It's been brutal and demanding which is what you expect when New Zealand teams play each other.
English trio George Kruis, Alex Goode and Freddie Burns have also all signed on for next season with Manu Tuilagi also linked with a move following his Leicester Tigers departure. It is an excellent environment with great coaching and an awesome bunch of dedicated players.
Fellow All Blacks Brodie Retallick and Sam Whitelock have similar arrangements allowing them to play in Japan while under contract to NZR.
Blues coach Leon MacDonald said he always expected to be without Barrett during the 2021 season.
"Our focus is fully on the current campaign but we have plans for next year without Beaudy".
But the fly-half will be available for the All Blacks global programme, the Auckland Blues confirmed.