The decision to remove Ms Joblin, who has been the board chairwoman for nearly seven years, was made by Mr Ryall.
Mr Stevens said he had had no idea Ms Joblin would not be returned as board chairwoman.
"I am lost at the minister's rationale.
"The board was reducing its debt and was meeting most of the Minister's targets - so why change things?
"It seems like a slap in the face for the whole board."
Mr Stevens said Ms Joblin had done a "fantastic" job.
But as a board member he would work with and support Ms McKinnon, who had not previously been a health board member.
Other board members were more guarded in their comments. Allan Anderson said choosing the board chairman was the Minister's prerogative.
"We [board members] have no input, and we are obliged to work with whoever the Minister appoints."
But Mr Anderson said it was a privilege to have had "the benefit of Kate's commitment and knowledge".
Philippa Baker-Hogan said the news was a surprise to her, "apart from some rumour".
Ms Baker-Hogan paid tribute to Ms Joblin and Ms McKinnon.
"I don't necessarily see this as signalling a change of direction for the board, but perhaps more a change in the way the new chair puts her stamp on the board ... time will tell."
Michael Laws said on his Facebook page that Ms McKinnon would "do a good job, but [it was a] surprising decision by the Government".
Judith MacDonald said the news was a "complete surprise".
"[It] was initially very disappointing as we had experienced good stewardship from Kate as chair."
She said there would be a period of adjustment for everybody, but once that was over "I'm quite sure we'll support Dot and get on with the challenges ahead".
In his statement, Mr Ryall said most health board chairs served a maximum of two terms. "While I've been the Minister of Health, Ms Joblin is the second longest-serving DHB chair in the country."
He said the appointment of Ms McKinnon was no reflection on Ms Joblin's performance.
"Ms Joblin did a very good job as chair of Whanganui DHB, and she now enters her second term as the deputy chair of MidCentral DHB." There were no plans to merge Whanganui and Palmerston North-based MidCentral DHB.
Ms Joblin declined to comment.
The new board will meet for the first time on December 13.