At least 13 people have been arrested in connection with three separate attacks on men of Mozambican, Guinean, Cuban, Turkish and Indian origin.
The attacks took place in Berlin and the cities of Weimar and Wismar.
They come days after the interior minister dismissed warnings that foreign fans were at risk of attack.
A report published by the German government earlier this week said racist violence increased by 23% last year.
But the attacks highlighted fears as Germany takes centre stage for the World Cup.