Captain Misbah-ul-Haq is highly unlikely to be available for his country's second test against New Zealand in Hamilton on Friday after having to return to Pakistan due to a family illness.

Misbah's father-in-law was critically ill and had been admitted to hospital and placed in intensive care, a Pakistan team spokesman said in an email to Reuters on Sunday.

The 42-year-old was due to leave New Zealand on Sunday evening and the spokesman said it would be "difficult" for him to return in time for the match at Seddon Park.

Misbah was missing from the post-match formalities after his side lost the first test by eight wickets to New Zealand at Hagley Oval in Christchurch on Sunday.

Vice-captain Azhar Ali, instead addressed the media and said their inspirational captain was heading home to deal with the issue.

"Unfortunately his father-in-law is very serious and he has to go back," Azhar said. "Hopefully things turn out well."

Azhar added Misbah would be a big loss for his side, if he did not make it back in time for the match. Travel time between the two countries is a minimum of 18 hours each way.

"We'll miss him definitely," Azhar said.

"We have to cope with that now and whoever comes into the side will take that opportunity and give us runs, as well as the stability he gives us in the middle."

New Zealand captain Kane Williamson said while Misbah's ability to galvanise his team and composed middle-order batting would be missed, he doubted the visitors would be under-strength for the Seddon Park game.

"Misbah is a fantastic leader, certainly a great middle order batter and a world class player," Williamson said.

"When you're without someone like that it is a loss. But (one of the) reasons why they're number two (in the world) is because they have depth and experience.

"I'm sure they'll find a suitable option for that middle order."