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Read suffered the injury in the Crusaders' 55-20 victory over South Africa's Southern Kings in Christchurch on Saturday.
"It is hugely disappointing that Kieran cannot join the team to South Africa," Crusaders coach Todd Blackadder said in a statement.
"He has been playing some brilliant rugby this season and it is unfortunate that this injury will keep him out of the game."
Read had not travelled with the Crusaders to South Africa, where they face the Stormers on Saturday and the Sharks on April 5 before playing the Western Force in Perth on April 13 on their way back to New Zealand.
Jordan Taufua was named to replace Read in the Crusaders' 26-man touring squad and fellow loose forward George Whitelock will assume the captaincy in his absence, the team added.
All Blacks flyhalf Daniel Carter has also not travelled with the team as his wife is due to give birth to their first child.
