Misbah, 40, hurt his hamstring whilst fielding in the second day-night international against New Zealand in Sharjah on Friday and had a scan which revealed the extent of the injury.
All-rounder Shahid Afridi will lead the side in the remaining matches, with the third in Sharjah on Sunday.
Khan said Misbah's injury was a big loss.
"It is a setback," Khan told reporters. "He has been advised to take a three to four week rest and will do his rehab under our physio Brad Robinson in UAE."
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"Misbah is the announced captain for the World Cup so we needed him at hand to discuss combinations for the World Cup and he would also be able to watch the players in the series," said Khan, also the chief selector.
"Misbah has always been keen on fitness and determined to recover in time so we hope he will have a speedy recovery."
The five-match series is currently tied at 1-1 after Pakistan won the first game in Dubai by three wickets while New Zealand won the second, also in Sharjah by four wickets on Friday.