Ban described reports of the incidents near Damascus on Wednesday as "very alarming and shocking" and urged the Syrian government to allow a United Nations inspection team, already on the ground in Syria, to begin an investigation without delay.
Footage distributed by activists showing people, including children, foaming around the mouth and doctors apparently administering oxygen to help them breathe, has triggered revulsion around the world.
Ban's comments, at a UN event in Seoul, put added pressure on Syrian President Bashar al-Assad after France denounced the "likely" use of chemical weapons.
"Any use of chemical weapons anywhere, by anybody, under any circumstances, would violate international law," Ban said. "Such a crime against humanity should result in serious consequences for the perpetrator.