Patel suffered an injury during the evening, preventing him from playing for New Zealand XI in the remainder of their four-day match against England, which had begun on the same day.
A statement from New Zealand Cricket said: "NZC understands that Jeetan Patel was refused entry to a bar in Queenstown.
"He subsequently fell and hit his head. Patel returned to the team hotel, felt unwell and took himself to A and E."
Patel said: "I am sorry for my behaviour that evening and I accept that it was totally inappropriate for me to be out drinking during a match where I was representing my country."
Vettori added: "My behaviour was completely unprofessional in going out, and I should have spent time with Jeetan in another way."
Spinner Vettori had already been ruled out of the Test series due to injury.