Phillips, who suffered the injury during the Major League Cricket final in Dallas, would require “several weeks” to recover, New Zealand Cricket said in a statement.
The 28-year-old will miss the tri-series, also involving South Africa, and the subsequent two-test series against hosts Zimbabwe.
New Zealand is already without batter Finn Allen, who was ruled out of the tri-series with a foot injury suffered in the MLC.
“It’s disappointing to lose someone of Glenn’s calibre,” head coach Rob Walter said.
“Much like Finn, we feel for Glenn and that he misses out on this series.
“We know he was eager to get out on the field for the Blackcaps, and unfortunately, he won’t be able to do that for this series.
“We know he’ll work hard to get himself back onto the park, and I look forward to when that happens.”
Phillips’ replacement in the test squad will be named later, the NZC added.
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