New WHO head Dr Tedros Adhanom Ghebreyesus praised Zimbabwe for its commitment to public health.
But critics say that during Mr Mugabe's 37-year rule Zimbabwe's health services have deteriorated, with staff regularly unpaid and medicines in short supply.
Dr Tedros, who is Ethiopian, is the first African to lead the WHO.
He was elected with a mandate to tackle perceived politicisation in the organisation.
Dr Tedros replaced Margaret Chan, who stepped down from her 10-year post in June.