At least 575 people have died from the disease, which has infected 12,700 people since August.
The Zimbabwean government has declared the epidemic a "national emergency" and appealed for international aid.
Speaking in Copenhagen, US Secretary of State Condoleezza Rice said: "It is well past time for Robert Mugabe to leave."
She said the stalled power-sharing talks and the mounting "humanitarian toll" in the country should spur international action and called on African leaders to take the lead.
Tutu, a one-time supporter of the Zimbabwean President, said Mugabe had ruined a "wonderful country".
British Prime Minister Gordon Brown also called on the international community to tell Mr Mugabe that "enough is enough".
"This is now an international rather than a national emergency. International because disease crosses borders," he said.
"International because the systems of government in Zimbabwe are now broken.
"There is no state capable or willing (to protect) its people."
He is destroying a wonderful country. A country that used to be a bread basket has now become a basket case itself needing help. (Archbishop Desmond Tutu on Robert Mugabe)
In another sign of mounting international pressure, the EU is considering stepping up sanctions against Mr Mugabe and other key figures in his regime.
Cholera, which is carried by contaminated water, has spread quickly in Zimbabwe where years of neglect of the basic infrastructure have resulted in a collapse of the water and sanitation systems.
Sewage is flowing in some of the streets in Harare, where most of the cholera cases have been reported, and clean drinking water is in short supply.
Hospitals across the country are struggling to deal with the influx of patients because of a shortage of re-hydration drugs and fluids.
There is also a critical shortage of medical staff, many of whom have walked out in protest at salaries so low that they do not even cover the cost of transportation to work.
Their wages are paid into bank accounts by the government, but with cash withdrawals rationed it is almost impossible to withdraw enough money to buy even small items like a loaf of bread.
South Africa’s government has agreed to send a crisis response team to Zimbabwe to help with the cholera crisis which has seeped over the border.
Almost 500 patients have been treated at an emergency cholera clinic in the town of Musina in the past two weeks.
Most of the patients are Zimbabweans who had entered South Africa illegally to find work, carrying the disease with them over the border.
South Africa’s leaders are still reluctant to bow to international pressure and openly criticise Mr Mugabe over the spiralling decline of Zimbabwe and the political paralysis in the country.
Former President Thabo Mbeki, the official mediator, has instead blamed opposition leader Morgan Tsvangirai for the impasse, accusing him of refusing to compromise over the flawed power-sharing deal that would effectively leave Mr Mugabe in control of the country.