The death of the 23-year-old prop was announced by his family, the Blues and New Zealand Rugby on Saturday.
"Michael was a talented athlete and our focus is to offer our support and sympathy for the family, and we are supporting our team and staff, some of whom are currently overseas," Blues Chief Executive Michael Redman said in a statement.
The Blues face the Jaguares later on Saturday, having travelled to South Africa last week where they lost 26-7 to the Sharks.
Tamoaieta was a squad member of the Blues last season and made two appearances for the team, but was not in the initial squad for the 2019 season.
New Zealand Rugby Chief executive Steve Tew said the national body was saddened by the death of Tamoaieta, who played for New Zealand Secondary Schools and for the North Harbour provincial side.
"Our sincerest condolences are with Michael's family at this very sad time," Tew said.
"Michael was a valued member of the Blues and North Harbour rugby environments and had been part of the New Zealand Secondary Schools team.
"We know his family, club and former school mates will be feeling this loss and our thoughts are with them all."
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