The powerful back rower, who is expected to be out for six months, will need surgery after a bone fragment was knocked off his shoulder joint in the Blues' loss to Waikato Chiefs in the second round of fixtures.
Kaino was already carrying a slight injury to the left shoulder and after taking the blow he continued to play, not realising the severity of the issue.
"I'm gutted," Kaino said in a statement. "I really didn't think this was going to take me out of the whole Blues season,"
Auckland have had a slow start to the season but picked up their first win of the championship on Saturday in South Africa against the Bulls following two losses to New Zealand rivals Waikato and Canterbury Crusaders.
The three-times winners face the Stormers in South Africa on Friday.
"Jerome is a great player and brings a lot to the Blues on and off the field," coach Pat Lam said.
"This is a real blow for him and I know, like us, he is really disappointed that he won't be playing this season with the team. All of us wish him well for the surgery on Wednesday."
The loss of Kaino, who played in every match of New Zealand's successful World Cup campaign last year, could also prove a problem for the All Blacks.
New Zealand are due to play three home tests against Ireland in June before the expanded Tri-Nations series, now featuring Argentina, starts in August.