Angela Merkel made a short, emotional speech saying the camp “fills me with deep sadness and shame” and said it was a warning of the dangers of indifference.
The visit is part of Angela Merkel’s election campaign and was followed by a rally in a beer tent nearby.
Political opponents called the combination “tasteless”.
Some 30,000 people died in Dachau before it was liberated by US soldiers on 29 April 1945.
It was the first camp to be built by the Nazis in March 1933.
Angela Merkel, who toured the remnants of the camp, said it stood for “a horrible and unprecedented chapter of our history”.
“At the same time, this place is a constant warning: how did Germany reach the point of taking away the right of people to live because of their origin, their religion?”
Angela Merkel said the “vast majority of Germans” had closed their eyes to what was going on, and said her visit was intended “to be a bridge from history to the present and into the future that we want to continue to build”.
Max Mannheimer, the 93-year-old president of the Dachau camp committee, had long lobbied for Angela Merkel to go to the camp, near Munich in southern Germany.
He hailed her decision as “historic” and a “signal of respect for the former detainees”.
But a leader of the opposition Greens party, Renate Kuenast, described Angela Merkel’s programme of the camp visit followed by an election rally as a “tasteless and outrageous combination”.
“If you’re serious about commemoration at such a place of horrors, then you don’t pay such a visit during an election campaign,” she told the daily Leipziger Volkszeitung.
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