Jackson added: "I'm pretty sure he'll be fine for the Lions tour. He'll put his feet up and normally you come back pretty quickly from those sorts of operations."
The Highlanders' Liam Squire is the obvious replacement for Kaino should he not be fit for the first test, and Akira Ioane replaces him at the Blues, albeit in the No8 jersey, starting with the match against the Brumbies in Canberra on Sunday.
"Jerome brings that attitude and aggression and physicality," Jackson said. "It is going to be a loss but it gives Akira an opportunity to get out there and show what he's got for 80 minutes. One, it's a loss, but two we're quite excited about seeing him [Ioane] go."
The Blues, just outside the playoff mix in ninth place, will be very much outside chances to make the finals now; in fact, Jackson believes they probably need to win their remaining seven matches with bonus points in order to do so.
The Blues will travel straight to Sydney for their match against the Waratahs the following weekend after the Brumbies match.
"Our goals are we probably need five points from every game. We just need to play and believe in ourselves. If we draw a line on the end of the season there's nothing to look forward to.
"Obviously we need some things to go our way but we can only control what we do now.
"They'll be seeing us as a wounded dog and they'll look at us to see if they can rectify their season and get them back on track as well."