The Tonga-born flanker or number eight won 17 Test caps for the All Blacks between 2005 and 2008.
In 2012, it was reported Lauaki - who played for Super Rugby club Chiefs as well as French sides Bayonne and Clermont - had been suffering from heart and kidney problems.
"The thoughts of everyone are with the family of Sione Lauaki. Gone too soon. RIP, Wax," tweeted the All Blacks.
The Chiefs were playing in the Brisbane Global Tens rugby tournament on Sunday and dedicated their victory to their former player.
"We lost a brother today,'' outside back Shaun Stevenson said after the Chiefs won the Brisbane title.
Earlier in the day, Chiefs coach Dave Rennie said his side would dedicate the to the tournament to the memory of Lauaki.
"There's a number of guys who played a lot of footy with Wax,'' Rennie said, referring to Lauaki's nickname. "There's a lot of motivating factors. Not everyone knows Wax, but he played a lot of footy for the Chiefs and he's certainly highly respected among his mates.''
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Former New Zealand forward Sione Lauaki has died at the age of 35.