Osvaldo, who joined in the summer from Roma, has scored four times for Mauricio Pochettino's side - including the equaliser against Manchester City in December.
The 28-year-old will sit out the FA Cup fourth-round tie with Yeovil, as well as Barclays Premier League fixtures against Arsenal and Fulham.
The club released a statement on Thursday confirming the Italy international will not be involved in the coming fortnight. No details of the incident have been disclosed.
"Southampton Football Club has today suspended striker Dani Osvaldo for two weeks, following an incident at the club's Staplewood training ground," the statement read.
"The club has taken swift and proper action for what it considers a breach of the conduct expected of its players.
"Southampton will be making no further comment at this time."
The Southampton club-record signing, who played under Mauricio Pochettino at Espanyol, was fined and suspended at former club Roma for punching team-mate Erik Lamela during a 2-0 defeat to Udinese.
The training ground incident is the latest story in a week which has seen Southampton make many headlines.
Nicola Cortese resigned as chief executive last week, sparking rumours about the futures of manager Pochettino and a number of their high-profile players.
Saints' owner Katharina Liebherr has moved to steady the ship and, with Pochettino insisting he will remain in charge of the team, things had appeared to calm down before Osvaldo's misdemeanour.