Mark Drakeford discovered William would be the new Prince of Wales at the same time as the public.
Mark Drakeford said he was not given advance notice that Prince William would be the new Prince of Wales.
Prince William and his wife Catherine were named the new Prince and Princess of Wales by King Charles III on Saturday.
The first minister said he had heard of the decision at the same time as the public.
When asked on BBC Radio Wales if he had been consulted on King Charles III’s decision, he said “no, not at all”.
Mr Drakeford said he and the Prince had a “very warm” conversation and there was time now for him “to get to know Wales better”.
The first minister confirmed he had spoken to the Prince of Wales on the telephone on Sunday.
He said: “It was a very warm conversation, Prince William was very keen to reflect on the time he and his family have spent in Ynys Mon. A period that clearly means a great deal to him and he looks back on with enormous fondness.
“Given that the announcement was made so early in the reign of the new monarch, I think we can be sure it was given a great deal of thought.”
There has been some debate over the future of the role of the Prince of Wales, but the first minister said that now was not the time for that conversation.
He said: “I think there is a debate there to be had, and it is absolutely proper. I don’t think the debate needs to come to a climax in this week of all weeks.
“If I were asked for advice, [it would be] that the new Prince of Wales takes the time he needs.
“To think through what he would will wish to achieve, to give himself the opportunity to become better acquainted with the Wales of today.”
He said the Prince was in a “reflective mood” and wanted to “look forward, talk about the time he needs to take on the responsibilities, and fashion the job in the way that will be right for him and Wales in the 21st century”.
An opinion poll of 1,020 people in June 2022, conducted by ITV and YouGov, suggested that 46% of people thought there should be another Prince of Wales, while 31% did not.