The federation said those who defied the order ran the risk of being banned from the game.
"Soccer players with ponytails hair-bands and sculpted beards will be banned from playing or will be fined Navid Majd head of the federation's public relations office told Reuters.
The ban does not apply to long hair.
"The Prophet Mohammad had long hair. We have no problem with it Majd said.
Some newspapers reported recently that at least two soccer players in the Iranian professional league had received warnings because of their "inappropriate" hair style. But Majd denied it.
Many Iranians are obsessed with soccer and soccer players are considered role models for younger fans.
"We should respect our culture especially our sportsmen Majd said.
Since the 1979 Islamic revolution conservatives have continually tried to hold back the tide of Western cultural influence and promote Islamic values.
A crowd of 110000 watched a match between Iran and Germany in Tehran earlier this month.
Iranian women were not allowed to see the match after the football federation upheld a ban on them entering stadiums even though women are the Islamic country's most passionate fans.