Woodcock, who has 110 caps, was initially named in the squad pending medical checks on his shoulder but the 33-year-old has now been replaced by the uncapped Joe Moody for the annual southern hemisphere competition against South Africa, Australia and Argentina.
One of the most destructive scrummagers in world rugby, Woodcock is key to Hansen's plans for the All Blacks' defence of their World Cup title in England next year and the coach said the enforced absence could turn out to be beneficial.
"Every dark cloud has a bit of silver lining and for him it will be the opportunity to do something he hasn't done for 12 seasons and that's get a good off-season," Hansen told Fairfax Media at the team hotel in Auckland of Woodcock's surgery.
"It will be important because it will freshen him up and I'm pretty sure he'll be hungry getting into it next year."
Hansen said it was likely that Wyatt Crockett would assume the starting loosehead prop role for the Rugby Championship opener against Australia in Sydney on Aug. 16.
Crusaders lock Bird was ruled out for about three weeks with a toe injury and replaced by Wellington lock Jeremy Thrush, who made his All Blacks debut last year.
"You're always going to lose somebody, it's a contact game, and it's unfortunate for Dom but it gives Thrushy an opportunity," Hansen said.
Flyhalf Dan Carter has already been ruled out of at least the first two games after breaking a bone in his leg during the Super Rugby final, though Hansen was not overly concerned at his absence.
Carter had only just returned to rugby after taking a six-month sabbatical to deal with a series of niggling injuries that had curtailed his appearances over the last three seasons.
"It's unfortunate for Dan he got injured but there's not too much you can do when somebody smacks you in the leg and breaks a bone," Hansen added.
"We're not too concerned about the injury other than it's happened and he's missing football.
"From a long-term perspective we know he'll be fine and come back in and we also know we've got able replacements."
The All Blacks will take part in a 'game of three halves' later on Friday, playing 40 minutes each against provincial sides North Harbour and Northland, who then play each other for 40 minutes.
Hansen said centre Conrad Smith, who broke his thumb during the test series against England in June, and flanker Sam Cane, who missed the series with a knee injury, would play about 60 and 40 minutes respectively on Friday as they work their way back to match fitness.
(Writing by Greg Stutchbury; Editing by Peter Rutherford)
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