Carolyn Still, 29, was held for using threatening words and behaviour during Mansfield Town’s Blue Square Bet Premier play-off semi-final against York City last night.
It is understood she received a caution for her behaviour in Grosvenor Terrace, next to York’s Bootham Crescent stadium.
She became the youngest chief executive in English football when she was appointed by Mansfield last September.
A police spokesman said: “A 29-year-old woman from Retford was arrested at 9pm on Wednesday 2 May 2012, on Grosvenor Terrace, York, for using threatening words and behaviour. She was given an adult caution before being released.”
Mansfield survived the game to hold York to a 1-1 draw.
The club has declined to comment, but John Radford, chairman of Mansfield Town, said in a statement on his Facebook page that Ms Still became involved in the “incident” after a player suffered an injury and it has since been “blown totally out of proportion”.
He said: “Disappointed by how our player was being treated she was reprimanded for a verbal retort to a police officer.
“This incident has been blown totally out of proportion over a light hearted, hot-headed quip in defence of our player. I commend the police for their common sense in dealing with the matter quickly and no charges have been made against our CEO.”