Vettori tweaked a hamstring while fielding in the two-wicket loss in Napier on Tuesday and has not recovered in time to lead the hosts in a must-win match at Seddon Park. Ross Taylor will take over as captain.
There is better news for opening batsman Jesse Ryder.
He missed the Napier match due to a bruised finger, sustained while playing in a domestic match for Wellington last Sunday, but a team spokesman today said he would take his place in the XI.
Ryder is expected to open the batting alongside Martin Guptill.
New Zealand's playing XI will not be confirmed until the toss.
There are overcast skies in Hamilton with play scheduled to start at 2pm.
Pakistan lead the six-match series 2-1.