The 40-year-old sustained the problem during Pakistan's four-wicket defeat in the second ODI in Sharjah on Friday.
Earlier on Saturday, it was announced by the International Cricket Council that Misbah had been fined 15 per cent of his fee for that match after showing dissent at being given out caught behind.
And there was further bad news for the veteran later in the day as the Pakistan Cricket Board (PCB) confirmed that he would be out for the remainder of the five-match series, which is currently tied at 1-1.
"Misbah-ul-Haq [will be] forced to sit out [the] remaining three ODIs against New Zealand due [to] the hamstring injury he sustained during [the] 2nd ODI," read a post on the PCB's official Twitter account.
"Shahid Afridi to be stand-in captain. No decision yet taken if Misbah will stay with the team in UAE or travel back to Pakistan."