As Mugabe flew to Singapore, nurses at public hospitals joined junior doctors in a two-week strike that is meant to pressure Mugabe's government into paying 2016 bonuses due in December.
Increasingly frail, Mugabe now struggles to walk and is seldom far from the arms of an aide. His public speeches have become meandering and repetitive.
"His Excellency the President left for Singapore for a scheduled medical review. We expect him back in the country early next week," spokesman George Charamba said. He did not give details.
Mugabe frequently travels to Singapore for medical checks, with aides saying he suffers from an eye cataract. But reports in private media suggest he has prostate cancer, something Mugabe's office denies.
The veteran leader's critics say his overseas medical trips testify to the collapse of Zimbabwe's public health system since the economy started to fall apart in 2000.
The issue of succession to Mugabe, the only ruler Zimbabwe has known since independence in 1980, has divided the ruling ZANU-PF party into two camps, with one supporting Vice President Emmerson Mnangagwa and the other Mugabe's wife, Grace.