"I thought it's been a long time since Germany left (Nazi practices). We are mistaken," he said.
Several German towns prevented appearances by Erdogan's ministers last week, citing security and safety concerns.
The cancellations have infuriated the Turkish government, which accused Berlin of working against the "Yes" campaign in the referendum and summoned the German ambassador to the foreign ministry in protest.
"You will lecture us about democracy and then you will not let this country's ministers speak there," said an angry Erdogan, adding that Germany was not "respecting opinion and thought".
Chancellor Angela Merkel on Saturday called Turkish Prime Minister Binali Yildirim to try to defuse the row, and the two countries' foreign ministers are set to meet later this week.