The order, from the school's governing board and chairman Faruk Kahn, contradicts the policy of the Australian Federation of Islamic Councils.
AFIC assistant secretary Keysar Trad said the policy was at odds with the national federation, but it was powerless to intervene.
"I'm aware there's a policy at that school with respect to the scarf," Mr Trad said.
"The AFIC policy is not to require any teacher to observe the hijab. In SA, the board itself has decided they want to operate in their way and we are not allowed to interfere in the matter.
"We maintain that staff should dress modestly but not be required by the nature of policy to wear the hijab."
Mr Trad said that matters of unfair dismissal resulting from teachers disobeying the school's hijab policy should be referred to Fair Work Australia.
"It's confusing for our children to see their teachers wearing the scarf in school and then they take it off when they are out shopping and the children see them there," he said.
"It is also a respect thing for our staff. If they are not Muslim they should not be forced to dress as Muslim."
One long-term teacher at the Islamic College of SA said a new school board was now "forcing teachers to put hijabs back on".