The 24-year-old bowled briefly in the warm-up but was restricted by the same niggle and ruled himself out of contention after consulting with team sports science guru Alex Kountouris.
Richardson will undergo scans at some point but it is a long weekend in New Zealand because of Waitangi Day.
It is highly unlikely that Richardson will feature in the ODI series finale on Monday.
Australia’s T20 World Cup campaign starts on March 18 in the northern Indian town of Dharamsala, giving Richardson plenty of time to recover if it is a minor issue.
However, Cricket Australia will always take a conservative approach with any injury – let alone a paceman with a history of back trouble.
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“He pulled up with a bit of a sore back,” Steve Smith said of Richardson.
Richardson was diagnosed with a back ‘hot spot’ while playing for Australia A in 2013.
In 2014, he was also sidelined during an ODI tri-series in Zimbabwe.
“I’ve always had things like this as a kid and it’s one of those things if the physio gives you the all clear you go for it,” Richardson said at the time.
National T20 captain Aaron Finch and gun allrounder James Faulkner are currently on the sidelines because of hamstring injuries.
However, it is Australia’s pace attack that has been decimated following the retirement of Mitchell Johnson.
Mitchell Starc and Pat Cummins, both part of Australia’s triumphant ODI World Cup squad last year, will miss the T20 World Cup.
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Nathan Coulter-Nile is also sidelined through injury, while James Pattinson is back on the park but failed to play a single Big Bash League match because of shin soreness.
“If I’m fit and bowling I always want to play all three forms of cricket for Australia. That’s my goal,” Pattinson said, when asked about his chances of playing the T20 World Cup.