A spokesman said Britain has raised concerns with the WHO over the Zimbabwean president's new role, warning that it risks undercutting the organisation's good work.
Mr Mugabe has long faced EU and US sanctions over human rights abuses.
Commenting on his appointment, the UK Government spokesman said: "We have registered our concerns with WHO director general Dr Tedros Adhanom Ghebreyesus.
"Although Mugabe will not have an executive role, his appointment risks overshadowing the work undertaken globally by the WHO on non-communicable diseases."
Mr Tedros, an Ethiopian who became the WHO's first African director-general this year, said Mr Mugabe could use his role "to influence his peers in the region" and said Zimbabwe was "a country that places universal health coverage and health promotion at the centre of its policies".
But despite once being known as the breadbasket of southern Africa, in 2008 a charity released a report documenting failures in Zimbabwe's health system and blamed Mr Mugabe for what it called a man-made crisis.
Physicians for Human Rights found his government had "presided over the dramatic reversal of its population's access to food, clean water, basic sanitation and health care".
It went on: "The Mugabe regime has used any means at its disposal, including politicising the health sector, to maintain its hold on power."
The report said Mr Mugabe's policies had led to "the shuttering of hospitals and clinics, the closing of its medical school and the beatings of health workers".
The Zimbabwean leader's appointment as WHO goodwill ambassador was announced at a conference in Uruguay.
The UN and its agencies appoint goodwill ambassadors to draw attention to issues of concern, but they are generally seen as honorary roles with little real power.