The park was filled 3,000 Muslims celebrating an Islamic holiday.
The women were told they could not wear their traditional head-covering called Hijabs on some rides.
Park officials were in the process of issuing refunds when members of the Muslim group got into a scuffle with each other.
Members of the tour group maintain that security guards pushed a woman to a ground and that's what started the fight.
The park spokesman says Playland doesn't allow headgear on rides for safety reasons.
"This misunderstanding was very unfortunate," said Peter Tartaglia, Deputy Parks Commissioner. "Our headgear policy is designed to protect the safety of patrons and safety is our first concern. This policy was repeatedly articulated to the tour operator, but unfortunately the message did not reach some of the members of his group."
Twelve people from Brooklyn, two from Valley Cottage and one from Staten Island were arrested.
Beshar Ali and Alansi Salah, both of Brooklyn, faced the most serious charges of felony assault after allegedly attacking two park rangers who tried to break up the fight.
Most of the others were charged with disorderly conduct and related offenses.