The ICC was forced to issue a statement confirming it had been investigating a small group of players after a local newspaper reported that up to three players were involved in a probe by the Anti-Corruption and Security Unit.
NZC had also issued a statement before White gave a short media conference at University Oval in Dunedin before the third day's play of the first test between New Zealand and West Indies began.
"New Zealand Cricket is aware that the International Cricket Council is investigating a small number of New Zealand cricketers," White told reporters.
"We have been aware of this investigation for a number of months and are shocked and surprised by the allegations.
"I do know who they are but I can't name them because it is with the ICC," he added when asked if he knew who was the subject of the investigation.
White said it was his understanding that three players were under scrutiny. He would not comment on whether the players were aware that they were under investigation.
No current players are the subject of the probe and the matches under investigation were overseas and not domestic matches in New Zealand, he said.
He would not say in what years the players had appeared for New Zealand.
The ICC had kept NZC up to date with regular meetings, he added.
The ICC had earlier confirmed its investigation following the report in the New Zealand Herald.
"The ICC confirms that it has indeed been working closely over the past few months with its colleagues in the domestic anti-corruption units of member boards to investigate these and related matters," the statement said.
"The ICC and all of its members maintain a zero-tolerance attitude towards corruption in the sport, and the ACSU will continue to collaborate with relevant individuals in order to complete its investigation process.
"Naturally, as the investigation remains ongoing and nobody has been charged with any offence, no further comment will be made."
(Reporting by Greg Stutchbury; Editing by Ed Osmond)
