The Houthi delegation, which was due to arrive on Sunday, was still in Djibouti in east Africa on Monday evening.
Mr Ban warned that "while the parties bicker, Yemen burns" and urged an immediate humanitarian ceasefire.
An estimated 20 million Yemenis are in need of aid following months of fighting in the country.
The humanitarian situation has been described as "catastrophic" by the UN, with more than 2,000 people killed in the conflict.
Opening the talks, Mr Ban said: "Today Yemen's very existence hangs in the balance."
He urged action on three main areas: "First, a renewed humanitarian pause to allow critical assistance to reach all Yemenis in need and provide a respite for Yemenis as the holy month of Ramadan begins.
"Second, I urge the parties to reach agreement on local ceasefires. Third, I call on them to resume a peaceful and orderly political transition and to ensure that the process includes more representation from other political parties, women, youth and civil society."
The BBC's Imogen Foulkes in Geneva said the Houthi representatives were apparently delayed over what airspace their plane could fly through. She said that the confusion did not bode well for the talks.
A Saudi-led coalition of Arab states has been bombing the Houthi rebels and their allies since March.
The bombing campaign was launched to support Yemeni President Abdrabbuh Mansour Hadi, who escaped to the Saudi capital, Riyadh, when the Houthis advanced on his stronghold in Aden in southern Yemen.
In recent weeks, fighting between Saudi forces and the Houthis has intensified on Yemen's border with Saudi Arabia.
On Saturday, Saudi Arabia claimed to have shot down a Scud missile fired by the Houthis.
The attack followed fighting on the border on Friday, in which four Saudi soldiers and a number of Yemeni rebels died.
On the same day, bombs hit the Old City of Yemen's capital, Sanaa, killing five people according to local sources.
UN Secretary General Ban Ki-moon has opened talks in Geneva on the conflict in Yemen but without the presence of Houthi rebel representatives.