Wagner is expected to be ruled out of action for more than five weeks, New Zealand head coach Gary Stead confirmed on Thursday.
The world's third-ranked Test bowler endured fractured toes when he suffered a blow to his right foot from a Shaheen Afridi yorker while batting in the first innings.
Wagner then required pain-killing injections to send down 21 overs in Pakistan's first innings and 28 in the second to seal a dramatic victory for New Zealand.
Wagner's four wickets across the game included the prized scalp of Fawad Alam on the final day when he had the second-innings centurion caught behind off a menacing bouncer.
The important breakthrough hastened Pakistan's slide and foiled the tourists' attempts at earning a hard-fought draw.
"The injections he was getting were wearing off each time so he was getting less and less (pain-free) time and we can't have him going through that again for this Test match," Stead said as the home team reached Christchurch ahead of the second Test match.
"Everyone knows Neil plays with his heart on his sleeve and he just showed how tough he really is and how valuable he's been to New Zealand for a long, long time and we'll miss him enormously.
"We want to be sensible about it. He probably needs five or six weeks of healing now to be right for the end of the season."
Wagner's remarkable exploits in the face of searing pain were lauded by Kane Williamson and opposing skipper Mohammad Rizwan alike, who termed him "mad" having bowled well with "attitude and aggression".
New Zealand have not named any replacement for the left-arm quick but it is likely another fast bowler will be inducted into the Test set-up.
The Hagley Oval pitch in Christchurch has traditionally favoured pace and bounce, which might prompt the hosts to persist with a four-pronged seam attack or even add fast bowling all-rounder Daryl Mitchell in place of spinner Mitchell Santner.
New Zealand will need to sweep the series 2-nil in order to maintain hopes of making it to the World Test Championship final at Lord's next summer.