Ban laid flowers at the executions wall, where thousands of inmates, mostly Polish resistance members, were shot.
He then went to nearby Brzezinka village, home of the former Birkenau death camp, with its crematorium ruins and a monument to the victims.
"Auschwitz-Birkenau is not simply a register of atrocities. It is also a repository of courage and hope. Today I say loud and clear: Never again," Ban said.
He also visited the Chevra Lomdei Mishnayot synagogue, the only remaining building that testifies to the pre-war vibrant Jewish life in the town of Oswiecim.
In its guest book, Ban wrote that he was leaving "saddened but also with huge determination to build this world of equality, human dignity and peace," according to an image of the entry made available by the Jewish Center in the town.
Between 1940-1945, some 1.1 million people, mostly Jews, died in gas chambers or from starvation, disease and forced labor in Auschwitz and the adjacent Birkenau death camp that Nazi Germany built in occupied Poland.
Ban also visited Krakow, 50 kilometers (31 miles) from the Auschwitz memorial.
On Tuesday he will join a U.N. climate conference in Warsaw.
Boutros Boutros-Ghali was the first U.N. secretary general to visit Auschwitz in 1995.