The Saints striker made his fifth appearance for the club in today's 2-0 win over Swansea City, coming off early in the second half after taking a minor knock.
However, manager Mauricio Pochettino insisted that his substitution was largely tactical, and that Osvaldo will be fit to link up with the Azzurri tomorrow.
Dani is in Italy's 29-man squad for their games against Denmark next Friday and Armenia the following Tuesday.
Cesare Prandelli's side have already qualified for next summer's World Cup finals, but will be keen to end their Group B campaign on a high note.
Osvaldo is due to link up with his compatriots tomorrow in Florence before they transfer to Copenhagen on Thursday for their game at the Parken Stadium the following day.
The squad then returns to Italy, where they face Armenia at the Stadio San Paolo in Napoli on Tuesday 15th October.
The Azzurri have 20 points from their first eight qualifying games, securing their ticket to Brazil with a win over the Czech Republic last month.
Osvaldo, who currently has ten caps and three international goals to his name, will then return to Southampton ahead of our trip to Manchester United on Saturday 19th October.
The striker is not the only Saints player in international action over the coming ten days. Artur Boruc (Poland), Maya Yoshida (Japan), Dejan Lovren (Croatia), Rickie Lambert (England), Steven Davis (Northern Ireland), Gastón Ramírez (Uruguay), James Ward-Prowse, Luke Shaw (both England Under-21s), Calum Chambers, Matt Targett (both England Under-19s), Lloyd Isgrove (Wales Under-21s) and Chris Johns (Northern Ireland Under-19s) are also due to link up with their respective squads over the next 24 hours.