Saints drew 1-1 in Barclays Premier League action that day but club record signing Osvaldo, wactching from the sidelines after already being substituted, reacted angrily to a nasty tackle in stoppage time.
The 27-year-old's ban takes immediate effect after the charge of violent conduct was proved by an FA independent regulatory commission hearing.
Osvaldo is therefore ruled out of tomorrow's third round FA Cup clash with Burnley at St Mary's Stadium.
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.
Newcastle coach Woodman has been fined £1,250 and warned as to his future conduct after he admitted a charge of improper conduct.
Osvaldo, fit again after illness, will miss Saturday's FA Cup clash and Barclays Premier League matches against West Brom and Sunderland.
He will be free to play in Southampton's home Premier League fixture against Arsenal on January 28.