The backlash comes after the International Football Association Board upheld a Canadian referee's decision to send an 11-year-old girl from the pitch for refusing to remove her headscarf.
The board met to discuss the issue after Asmahan Mansour was sent off during an indoor tournament in the Montreal suburb of Laval in February.
Brian Barwick, the chief executive of the English FA, said that although it was important to respect religious customs, there was "a set of rules and laws" that must be adhered to. The ruling, which allows the hijab to be banned on health and safety grounds, applies to all organised football, including lessons, tournaments and after-school clubs.
But community groups believe it sends out a hostile message and will discourage girls from taking part.
Abdul Ahmed, football manager of community group Elite Youth, said the decision would make it more difficult to attract Muslim girls to the sport.
He said: "Parents can be nervous about letting their daughters play in tournaments away from home. This will make them less likely to consent."
Rimla Akhtar, who chairs the Muslim Women's Sports Foundation and plays football wearing a hijab, said the scarf presented no danger provided it was securely attached. Piara Power, director of the anti-racist campaign group Kick It Out, said: "Research shows young women who play sport are less likely to get into abusive relationships and more likely to go on to university. The last thing we should be doing is putting up more barriers."
The Association for Physical Education advises teachers to allow pupils to wear the hijab where possible, but to ask them to sit out if the activity is deemed too risky.
Practice varies from school to school. Some teach in single-sex groups, others allow girls to wear the hijab provided that it is securely pinned.
Last month, the Government caused controversy when it issued guidance allowing schools to ban the niqab, the Islamic face covering, on safety and security grounds.