Smith previously captained the side before facing the consequences for his involvement in the infamous ball-tampering scandal in 2018.
Smith was handed a suspension for 12 months with co-conspirators Warner and Bancroft also copping bans for their involvement in the debacle.
Australia's ODI series against New Zealand was cancelled following the first match while their proposed Test tour of Bangladesh hangs in uncertainty
Maxwell complained about mental exhaustion and excused himself from competitive cricket midway through his team's T20I series against Sri Lanka.
New Zealand faced a humiliating defeat by 71 runs and were due to play the second and third game on March 15 and 20 respectively.
"Once the test results are received and diagnosed, his return to the team can be determined," NZ Cricket said in a statement.
After New Zealand earlier kept the home side to 258 for seven, the Australian bowling attack dominated the Kiwi batsmen
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