Mr Ki-moon said the country must grant them access to the site near Damascus 'without delay' after men, women and children were killed as they slept after rockets were fired over the area.
He has asked the UN High Representative for Disarmament Affairs, Angela Kane, to travel to Damascus to push for access for the team, which arrived in Syria on Sunday to investigate several previous claims of chemical weapons use.
The poisoning deaths of many hundreds of people took place only three days after a team of U.N. chemical weapons experts arrived in Syria. But their limited mandate means the inspectors have so far been powerless to go to the scene, a short drive from where they are staying.
Syrian President Bashar al-Assad's government is under increasing pressure from Western and Gulf Arab countries and Assad's ally Russia to allow access to the rebel-held site of Wednesday's pre-dawn attack. The opposition Syrian National Coalition has also urged U.N. access.
"The Secretary-General believes that the incidents reported yesterday need to be investigated without delay," Ban's press office said in a statement. "A formal request is being sent by the United Nations to the government of Syria in this regard. He expects to receive a positive response without delay."
Syria's government offered no immediate public response to calls on Thursday for the U.N. team to inspect the site.
Assad opponents gave death tolls from the attack ranging from 500 to well over 1000 and said on Thursday that more bodies were still being found. The Syrian government has repeatedly denied using chemical weapons.
The U.N. team, led by Swedish scientist Ake Sellstrom, is already looking into three claims of chemical use in Syria's conflict. The United Nations has received a total of 14 reports of possible chemical attacks - one from Syria's government and the rest from Britain, France and the United States.
The Syrian government and the opposition have accused each other of using chemical weapons, and both have denied doing so. The UN inquiry will try to establish only whether chemical weapons were used, not who used them.
Ban said on Monday that if the experts found that chemical weapons had been used then it would be up to "the international community to determine what course of action should be taken to prove ... accountability and what needs to be done."
"Use of chemical weapons is a violation of international law and international human rights law," Ban told a news conference.
The United Nations has been demanding unfettered access in Syria to conduct the investigation. Sellstrom's team consists of experts from the Organization for the Prohibition of Chemical Weapons and the World Health Organisation.
Ban appointed Sellstrom to lead the inquiry in March, but diplomatic wrangling and concerns over safety prevented his team from entering Syria until this week.
"We're being exterminated with poison gas while they drink their coffee and sit inside their hotels," said Bara Abdelrahman, an activist in one of the Damascus suburbs where rebels say government rockets brought the poison gas that killed hundreds of people.
The Syrian government denies it was behind the mass killing, the deadliest incident of any kind in Syria's two-and-a-half year civil war and the worst apparent chemical weapons attack since Saddam Hussein gassed thousands of Iraqi Kurds in 1988.