Wicketkeeper Wade was promoted to captain after injury prevented Steve Smith from going on tour and his deputy David Warner was rested for the three limited-overs games.
But Wade hurt his back preparing for the opening match in Auckland on Monday and missed the six-run loss.
"After further discussions following his failure to recover sufficiently for Thursday's game two in Napier it was decided he will return to Melbourne for treatment," Cricket Australia said.
"It's not a major injury but with the short turnaround between matches and the four-and-a-half hour journey by bus to Hamilton for the next match, it's been decided it's best for me to go home and get some treatment," said Wade.
He added that he was confident of being fit for Australia's upcoming Test tour of India and a pre-series training camp in Dubai.
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