Video footage circulated widely on social media which showed the 24-year-old Republic of Ireland international hitting Samu Costa in the face following a challenge by the Portuguese midfielder on 27 July against Real Mallorca.
The two then clashed on the ground, before team-mates had to pull them apart.
Costa also appeared to swing an arm after Molumby shoved his head into his opponent. He was not red carded, but was substituted at half-time following the incident.
A Football Association statement added: “He accepted that his behaviour during the fixture constitutes violent conduct. An independent regulatory commission imposed his sanctions at a hearing.”