Aaron Motsoaledi condemned "health tourism" while speaking in Zimbabwe.
President Robert Mugabe, who frequently receives treatment in Singapore, had left the meeting of health ministers when Dr Motsoaledi made the comments.
Mr Mugabe's spokesman has said that the president's doctor is not "is not only Zimbabwean, he is actually black… He is very, very, very black".
George Charamba made those comments to Zimbabwe's state-run Herald newspaper in May, insisting that President Mugabe was not turning his back on Zimbabwean medical help.
Nigeria's Muhammadu Buhari and Angola's José Eduardo dos Santos have also been criticised for seeking medical treatment abroad this year.
At this week's conference Dr Motsoaledi said:
"We are the only continent that has its leaders seeking medical services outside the continent, outside our territory. We must be ashamed of that."
"This is called health tourism. We must promote our own," he added.
Dr Motsoaledi also urged governments to increase funding to local facilities.