"Make sure you have copies of your birth certificate, national ID and two passport photos ready to avoid delays," they say.
Zimbabwe, a once-prosperous nation of 13 million people in southern Africa, has struggled since 90-year-old Mugabe defeated rival Morgan Tsvangirai in a 2013 vote marked by allegations of irregularities. Mugabe's victory ended an uneasy power-sharing deal with the opposition, but foreign investors have been deterred by concerns about corruption and government policies to force foreign-owned and white-owned businesses to cede 51 percent of their shares to black Zimbabweans. Hundreds of manufacturing companies have closed in the past year.
Finance Minister Patrick Chinamasa has acknowledged the economy is struggling, cutting growth forecasts for 2014 by half to 3.1 percent. The World Bank forecasts 2 percent.
The fallout is putting pressure on the passport department, which is unable to meet demand even though it prints 3,000 passports a day.
"There is a high demand for passports in Zimbabwe as people are leaving to escape the economic crisis the country is facing," Registrar General Tobaiwa Mudebe, who heads the passport department, told a parliamentary committee in July.
Zimbabwe's exports are faltering. A massive debt means Zimbabwe cannot borrow enough money, even from allies such as China, to make ends meet. The United States has sanctions against Mugabe and his closest associates over human rights concerns. The government, which has blamed economic woes on Western sanctions, adopted the U.S. dollar as an official currency in 2009 to curb inflation that had soared to more than 1 billion percent.
Torn $1 and $2 notes are now the major currency on the streets. A growing scarcity of dollars has led some pro-government analysts and politicians to call for a return to the Zimbabwean currency.
Passports are only issued at the Harare office, so many people travel long distances.
Felix Zengeya, 30, came from Mutare city, 190 miles away, to try to replace his passport and return to South Africa, which has one of Africa's biggest economies. He had fled economic hardship in Zimbabwe in 2008, but returned when the economy improved. But now he has given up hope of getting a job in Zimbabwe's diamond mines.
He would leave his wife and 4-year-old daughter if he heads south again.
South Africa recently tightened immigration rules which could have frozen Zengeya and tens of thousands of other Zimbabweans living in that country under a 2009 special dispensation. But after pleas from Mugabe's government, South Africa has agreed to extend the special allowance for Zimbabwean immigrants to stay until 2017.
Yet, for Zengeya, his mind had been set even before the decision to relax immigration rules for Zimbabweans was made.
"I am going," he said. "Even without papers, I can find work."