Smith, who was raised in Oamaru, sustained the injury while batting on day two of the first test in Bulawayo.
A subsequent MRI has confirmed he picked up an abdominal strain which will require approximately two to four weeks recovery.
Zak Foulkes, who recently played in the T20I Tri-Series against Zimbabwe and South Africa, has been called into his first test squad to replace Smith.
Smith recorded three for 20 in Zimbabwe's first innings.
New Zealand won the test by nine wickets inside three days.
Meanwhile Auckland Aces Ben Lister has also been called in as additional pace cover for Will O'Rourke who experienced back stiffness on day three and is being monitored.
Captain Tom Latham also missed the opening test with a shoulder injury and it is unsure if he will be available for the second test which starts on Thursday.
