But Vaughan Gething added he believed there was still a case for increased medical education to take place there.
He said this could be delivered by Cardiff, Swansea and Bangor universities working closely together.
Plaid Cymru AM Sian Gwenllian, who had called for a medical school, said the decision "showed contempt for the people of north Wales".
One of Bangor University's top medics had said in May it was ready to host a new medical school.
Prof Dean Williams, head of the School of Medical Sciences, said Wales needed to expand medical schools to deal with future shortages of doctors, particularly GPs.
Ms Gwenllian, who commissioned his report, said of Mr Gething's announcement: "I was expecting to see at least some seeds sown to the establishment of a medical school in Bangor."
She said it showed "a lack of ambition in developing the health services for people in the north".
Mr Gething said Welsh Government officials had discussed the matter over a number of months with key stakeholders across north Wales, the wider NHS family and the two current medical schools in Wales.
"While I am not persuaded on the need for a new medical school, I do believe that there is a case for increased medical education to take place in north Wales," he said.
"A proposed collaborative approach to medical education and training in north Wales based upon Cardiff, Swansea and Bangor Universities working more closely can deliver the increase in medical education opportunities in north Wales.
"All parties have confirmed a willingness to work together to deliver programmes which would result in students having the option of spending a far greater period of their studies in north Wales.
"Establishing a medical school is a long and costly process; the proposal outlined above provides for a better use of resources and would deliver medical education in north Wales at a much greater pace."
There is no case for a new medical school to be set up in north Wales, the health secretary has said.