Around 250,000 turn out in two cities in support of a bid to join the UN.
“This has been the official position of the United Nations and has not changed since 1971,” Ban said on Tuesday.
“This matter … was very carefully considered by the secretariat, and in light of resolution 2758 it was not legally possible to receive the purported application for membership.”
Beijing regards Taiwan as part of its territory, and says it will use force if it declares independence.
Beijing and Taipei both claim they are the legitimate government of all China.
Taiwan has been a multi-party democracy since 1996.
Taiwan’s defence ministry says China now has nearly 1,000 missiles aimed at the island.
The US is Taiwan’s major arms supplier and has warned China that any attack would be viewed with “grave concern”.
The Marshall Islands, representing that group, has asked for Taiwan’s application to be considered by the new general assembly session.
A UN committee is expected to review the proposal on Wednesday.
But with China holding a veto in the 15-member security council and overwhelming support in the 192-member general assembly, Taiwanese officials say they know the UN bid will fail.
Despite this, Chen Shui-bian, Taiwan’s president, is planning to hold a referendum on whether the island should seek UN membership alongside presidential elections next March.
Beijing has threatened to use force if the island declares independence and UN membership could be considered a move towards that.
Mark Seddon, Al Jazeera’s correspondent at the UN, said the Chinese would take a hard line on Taiwan but were unlikely to launch military action.
“They have been increasing the number of missiles aimed at Taiwan, quite considerably in fact, but to take on Taiwan is another matter entirely,” he said.
I think there is a lot a sabre-rattling going on … and don’t forget the United States is actually treaty-bound to defend Taiwan if it is attacked.”