In a tweet, WHO director-general Tedros Adhanom Ghebreyesus said: "I'm listening. I hear your concerns. Rethinking the approach in light of WHO values. I will issue a statement as soon as possible."
Mr Mugabe, 93, has long been criticised at home for going overseas for medical treatment and for presiding over the collapse of his country's healthcare system.
I’m listening. I hear your concerns. Rethinking the approach in light of WHO values. I will issue a statement as soon as possible— Tedros Adhanom (@DrTedros) October 21, 2017
The world's oldest head of state also faces US sanctions over his government's human rights abuses.
Announcing his appointment at a conference in Uruguay, Dr Tedros said Mr Mugabe could use the role to "influence his peers in his region" to combat non-communicable diseases.
He went on to describe Zimbabwe as "a country that places universal health coverage and health promotion at the centre of its policies."
Britain said Mr Mugabe's appointment was "surprising and disappointing" and added that it risked overshadowing the WHO's global work. The United States said it was "disappointed."
Two dozen organisations — including the World Heart Federation and Cancer Research U.K. — released a statement slamming the appointment, saying health officials were "shocked and deeply concerned" and citing his "long track record of human rights violations."
The heads of UN agencies and the UN secretary-general typically choose celebrities and other prominent people as ambassadors to draw attention to global issues of concern, such as refugees (Angelina Jolie) and education (Malala Yousafzai). The choices are not subject to approval.
The ambassadors hold little actual power and also can be fired.
Zimbabwe was once was known as the region's prosperous breadbasket. But in 2008, the charity Physicians for Human Rights released a report documenting failures in the southern African nation's health system, saying Mr Mugabe's policies had led to a man-made crisis.
"The government of Robert Mugabe presided over the dramatic reversal of its population's access to food, clean water, basic sanitation and health care," the group concluded. Mr Mugabe's policies led directly to "the shuttering of hospitals and clinics, the closing of its medical school and the beatings of health workers," it added.