The Argentinian has been found guilty of violent conduct following the touchline fracas that marred the end of Southampton's 1-1 draw at Newcastle United on December 14.
In addition to his suspension, Osvaldo has been fined £40,000.
Newcastle United goalkeeping coach Andy Woodman, who was also involved in the incident, has been fined £1,250 and warned to his future conduct.
Woodman admitted a charge of improper conduct.
An FA statement on Friday read: "Following an Independent Regulatory Commission hearing today, Southampton's Dani Osvaldo has been suspended for three matches with immediate effect and fined £40,000 after a charge of violent conduct against him was found proven.
"Osvaldo was charged by The FA following an incident which occurred in or around the 94th minute of his side's game at Newcastle United on 14 December 2013.
"Newcastle United coach Andy Woodman, who was sent to the stands following the same incident, has been fined £1,250 and warned as to his future conduct after he admitted a charge of improper conduct."
Speaking to the media after the game, Newcastle manager Alan Pardew played down the ugly scenes.
"It wasn't a brawl and the game wasn't spoilt by that; it was a bit of panto season and it shouldn't take the headlines," he said.
"The battle is on the pitch and that was a terrific one. The one on the sidelines was a bit pathetic, what I saw of it, and best forgotten.
"I had my back to it most of the time. I said to their manager 'just get your staff and I'll get my staff', because we wanted to get on and win the game. He was of the same opinion as me."
