Woodman was sent to the stands following the clash during the Premier League clash with Southampton at St James’s Park.
Saints striker Dani Osvaldo has been charged with violent conduct as a result of the same incident.
Both men have until next Monday to respond.
FA statement: “Newcastle United coach Andy Woodman and Southampton player Dani Osvaldo have both been charged by the FA following an incident in the recent fixture between the two clubs.
“Osvaldo has been charged with violent conduct in relation to the incident in the 94th minute of the game at St James’s Park on Saturday, December 14.
“Meanwhile, Woodman, who was sent to the stands following the incident, has been charged with improper conduct. Neither club will face charges.
“Both parties have until December 23 to respond to the charges.”