Two other Plunket Shield matches have gone ahead as scheduled.
Northern Districts host Auckland at Tauranga's Bay Oval while Otago meet Canterbury in Queen's Park, Invercargill.
NZC also said it was in contact with the touring Pakistani men's and women's national teams who are in Nelson and Christchurch respectively.
The first test between the Black Caps and Pakistan is set to begin at Christchurch's Hagley Oval on Thursday.
Pakistan's team manager Wasim Bari confirmed to Cricinfo that all members of the squad are safe in Nelson, where their wartm-up game against New Zealand A was rained off.
"We felt the first tremors around 11.30pm," Bari told ESPNcricinfo.
"Some of the boys were in prayer, some were watching the India-England Test on TV when we felt the windows shake. The whole room began to shake. We were on the sixth and seventh floor, and evacuated immediately. The hotel staff was very helpful. We are all safe."
The Pakistan women's team just completed a ODI series in New Zealand and are staying on the 13th floor of a hotel in Christchurch. Manager Basit Ali told Geo News the squad were all safe but "still scared".
An All Blacks spokesperson said South Island and Wellington-based players were concerned about friends and family after learning of the quake en route from Rome to Dublin after their big win over Italy the day before.
Meanwhile, veteran broadcaster Keith Quinn tweeted a picture from his inner city apartment in Wellington of his rugby memorabilia strewn across the floor in his study.
World number one golfer Lydia Ko posted a message of support following the earthquakes.
