Clearfield Police Sgt. Kyle Jeffries said the alleged abuse did not happen at the Syracuse school where Fullmer teaches, but the victims is one of Fullmer's former students.
"We don't believe the owners of the business had any idea this was going on," Jeffries said.
Jeffries said Fullmer took advantage of his position of trust to get the girl to have a sexual relationship with him for about six months.
Jeffries said there is evidence of the crime in text messages exchanged between Fullmer and the girl.
Although police have no reason to believe there are other victims, they made the arrest public to make sure.
"Parents need to talk to their children, especially in this case, to see if they did have contact with this suspect," Jeffries said.
On the day Fullmer was arrested, parents showed up at Evolutionary Martial Arts in Syracuse to find the school closed early.
They defended the school.
Ron Higginson, who takes his 6-year-old grandson to karate lessons, said he will not take the boy out of lessons despite the news.
He said Fullmer was always professional when he was around him.
Higginson said the arrest does not change his opinion of the school.
"It's a great school,"he said.