The ICC and New Zealand Cricket were forced to reveal the investigation had been ongoing for months earlier on Thursday after a report in a local newspaper.
Neither the ICC or NZC would identify the three players involved but Vincent issued a short media statement on Thursday confirming he was co-operating with the investigation.
"I wish to let everyone know that I am cooperating with an ongoing ICC Anti-Corruption investigation that has been made public today," Vincent said in a statement issued through the New Zealand Cricket Players' Association.
"This investigation is bound by a number of rules and regulations that mean I am unable to make any further public comment.
"I will personally talk to the public when I am able to. In the meantime I cannot comment. Please respect me and my family's privacy until such time."
The names of the other two players have been reported by local and international media outlets but NZC would not confirm their identities when contacted by Reuters.
A NZC spokesperson referred the queries to the world governing body, who were unavailable for comment.
Earlier NZC chief executive David White had appeared at a hastily arranged media conference shortly before play on the third day of the first Test between West Indies and New Zealand at University Oval in Dunedin.
"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."
White said no current players are the subject of the probe and the matches under investigation were overseas and not domestic matches in 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."