Osvaldo, an Argentina-born Italian international, was watching from the sidelines after already being substituted during the 1-1 draw on 14 December when he reacted angrily to an aggressive tackle in stoppage-time.
The ugly scenes were sparked by Southampton midfielder Morgan Schneiderlin's yellow card for a late challenge 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 a Football Association independent regulatory commission hearing.
The 27-year-old, who joined Southampton for a club record £12.8m in August last year, is ruled out of Saturday's FA Cup third round tie against Burnley.
Newcastle coach Woodman has been fined £1,250 and warned as to his future conduct after he admitted a charge of improper conduct.
Osvaldo will miss the Burnley match and Premier League fixtures against West Bromwich Albion and Sunderland. He will be able to play in Southampton's home Premier League fixture against Arsenal on 28 January.