The latest period of detention started on May 30, 2003 when she was put back under house arrest "for her own protection" after clashes between her followers and government supporters in the northern town of Depayin.
On Tuesday, police also detained more than a dozen members of her National League for Democracy (NLD) party after they marched from the party's headquarters to her home.
Ban said that while he was in Myanmar last week he briefly raised the issue of her ongoing arrest.
But he said he felt it was not an appropriate time to focus on the matter beacuse he was there in an attempt to convince Myanmar's military rulers to allow aid into the country in the aftermath of Cyclone Nargis.
The official death toll from the cyclone stands at 78,000, with more than 1.5 million estimated to be displaced.
"I made it quite clear to them [the military government] that I was there for purely humanitarian grounds," he said.
The UN says the sooner Suu Kyi is freed the sooner Myanmar can move towards democracy.
But the actions of Myanmar's military suggest it has little interest in releasing one of its strongest opponents.
The UN said on Tuesday that Myanmar's military government was following up on a promise to allow in international relief workers to assist those affected by Cyclone Nargis.
The government appears, however, to have relaxed restrictions on foreign aid workers entering the country.
The UN humanitarian chief said a significant number of visas were now being granted to international aid workers to help cyclone survivors.
John Holmes told reporters on Tuesday that the United Nations had not seen "any blockages yet" in the granting of visas.
He said the world body estimates that up to 1.5 million people have received nothing or very little aid since the cyclone hit more than three weeks ago.
The apparent breakthrough in the flow of aid came after promises made by Myanmar's ruling generals to Ban who returned to New York on Monday after a four-day visit to Myanmar.
Ban said on Tuesday that the trouble-free access of some international aid workers into Myanmar's cyclone-ravaged Irrawaddy delta marked "a new spirit of co-operation" between the country's military government and the international community.
Myanmar earlier ignored international calls to delay a recent referendum on a military-backed constitution.
The military government was criticised for holding the referendum in the aftermath of the cyclone.
Aung San Suu Kyi's party rejected the outcome of Myanmar's referendum, calling the approval of the text a "sham".
|Myanmar activists living in Thailand have called|
for the release of Aung San Suu Kyi [EPA]
"The referendum is not free and fair," the party said in its first official reaction to the government's claim of victory.
The military government said on Monday that voters overwhelmingly approved the constitution that critics say will perpetuate the military's decades-old grip on power.
The generals said the constitution was approved by 92.5 per cent of voters.
The proposed constitution guarantees 25 per cent of parliamentary seats to the military and allows the president to hand over all power to the military in a state of emergency.
The new charter would also bar Aung San Suu Kyi from running for president.
Critics say these provisions go against the military government's professed commitment to democracy.