Scuffles broke out on Friday evening as thousands of England supporters gathered for Saturday's game while German fans celebrated their team's 4-2 win on penalties over Argentina in Berlin.
A spokeswoman for the British Home Office working in Germany said 13 English fans had been held, 10 for throwing bottles and three for minor offences. Of the 10, four were preventative arrests meaning they are likely to be released with no charge.
Twenty nine German fans were also held, she said.
The fans had been drinking and playing football together earlier on Friday but riot police had to move into the area and separate the two groups after they began throwing bottles.
Between 50,000 to 70,000 English fans have followed their side at each World Cup game in Germany and there has been little trouble but some 500 were held in Stuttgart before England's second-round match for clashing with rival fans and police.
England play Portugal at 1500 GMT in the Arena AufSchalke.
