The meeting with Ibrahim Gambari on Saturday was the first contact for the politician with an outsider in three years, a government source in Myanmar, also known as Burma, said.
The meeting followed an audience with Than Shwe, head of the military government, in Myanmar’s new jungle capital.
The talks lasted for about an hour.
Suu Kyi, a Nobel peace laureate, has been in prison or under house arrest for the past three years, with her telephone disconnected and all visitors barred apart from her housemaid and doctor.
Gambari, undersecretary-general for political affairs, is the first senior UN official to be allowed into Myanmar for more than two years.
The United States had insisted he be allowed to meet Suu Kyi, but leaders of her National League for Democracy (NLD) party, which won a 1990 election by a landslide only to be denied power by the army, had not been optimistic.
Gambari said after meeting her that Suu Kyi was in good health. He also said: "She feels she has a contribution to make and I hope she will be allowed to make it."
The army has run the Southeast Asian nation under various guises since a 1962 coup, during which time the economy has collapsed.
Gambari will brief foreign diplomats later on Saturday on the talks.