Saints secured a 1-1 draw at St James' Park but club record signing Osvaldo, watching from the sidelines after already being substituted, reacted angrily to a nasty tackle in stoppage time.
Unsavoury scenes were sparked by Southampton midfielder Morgan Schneiderlin's yellow card for a late tackle on Newcastle defender Massadio Haidara.
Staff and players from both benches became embroiled in a touchline ruckus, with referee Mike Jones sending Newcastle coach Andy Woodman and Saints back-room staff member Toni Jimenez to the stands.
Osvaldo's ban takes immediate effect after the charge of violent conduct was proved by an FA independent regulatory commission hearing.
The 27-year-old, fit again after illness, is therefore ruled out of Saturday's third round FA Cup clash with Burnley at St Mary's Stadium and Premier League matches against West Brom and Sunderland.
The Argentine-born Italian will be free to play in Southampton's home Premier League fixture against Arsenal on January 28.
Newcastle coach Woodman has been fined £1,250 and warned as to his future conduct after he admitted a charge of improper conduct.