Ban told reporters that he had met with Mugabe on Sunday on the sidelines of the African Union summit in the Ethiopian capital.
The meeting came three days after the country’s main opposition agreed to form a unity government with the 84-year-old president, a decision that Ban warned would not be enough to resolve Zimbabwe’s crisis.
"The humanitarian situation, which has reached an almost unbearable point for the people in Zimbabwe, has been a source of deep, deep concern for the international community, for the United Nations," Ban told a press conference.
"He assured me that he and his country would be fully open to humanitarian work and activities," Ban said.
Mugabe agreed to accept a high-level UN team led by assistant secretary-general on humanitarian affairs Catherine Bragg, who would assess the crisis and find ways to deliver aid, Ban said.
A cholera epidemic has killed more than 3 000 people in Zimbabwe, while 7 million people – more than half the population – need emergency food aid, according to UN figures.
Unity deal ‘imperfect’
Ban also repeated his concerns about the planned unity government, and said he had told Mugabe that his government still needed to release political prisoners and end human rights abuses.
"I still believe that this is an imperfect decision," Ban said of the unity deal.
"I have urged President Mugabe to build up on this new develoment and try to make progress as soon as possible so that they can ensure full democracy and freedom," he said.
"I urge them to fully protect the human rights of the Zimbabwean people and release all prisoners who have been arrested over the last few months."
Opposition leader Morgan Tsvangirai agreed on Friday to join Mugabe in a unity government, serving as prime minister, following disputed elections last March.