The All Blacks host Declan Kidney's team for three Tests on June 9 in Auckland, June 16 in Christchurch and June 23 in Hamilton. Jane may not be available again until June 30.
Jane injured the ankle in the Wellington Hurricanes' 37-25 loss to the ACT Brumbies on Friday and his absence will cause concerns for new All Blacks coach Steve Hansen, who has just one fit winger in the extended 35-man training squad he named for two training camps before the Ireland series.
Jane and his Hurricanes team-mate Julian Savea were the only two specialist wingers included, though Hansen had said at the time of the squad naming he expected Waikato Chiefs utility back Richard Kahui to play on the wing.
Kahui, who normally plays centre for the Chiefs but played on the wing in the All Blacks successful
Savea is uncapped at All Blacks level and while Otago utilities Ben Smith and Tamati Ellison could slot into the position.
It is likely Hansen will be forced to bring two other players into the training squad before he names the final 30-man Test squad on June 3.
World Cup winners Zac Guildford and Hosea Gear are the most likely candidates to come into the squad.
Jane's Hurricanes team-mate Karl Lowe was also injured in the loss to the Brumbies, sustaining a knee injury that will keep him out for between four and six weeks, the Hurricanes said.
"It is disappointing for both CJ and Lowey to be out with injury but we have been in this situation before and it means the other guys need to step up which they will do," Hurricanes coach Mark Hammett said.
"Our medical team will monitor the two closely and work with them to get them back on the park when ready."