Giroud will now miss home matches against Fiorentina and Frosinone after the international break.
Giroud guided home a brilliant header from Davide Calabria's cross in the 40th minute to guarantee Milan at least fourth place and complete Italy's line-up in Europe's top club competition next season
The 2022 FIFA World Cup in Qatar has entered the knockout phase, and one of the top honours players will be competing for is the Golden Boot, awarded to the player with the most goals in the tournament.
Olivier Giroud became France's joint all-time top scorer when his double helped the holders start the defence of their World Cup title in style with a 4-1 comeback Group D win against Australia on Tuesday.
An Olivier Giroud hat-trick helps France brush aside Paraguay 5-0 in an international friendly at Rennes.
Arsenal were again indebted to Olivier Giroud after the Frenchman's 89th-minute strike secured a 2-1 victory at second-tier Preston North End in the FA Cup third round on Saturday.
Olivier Giroud's stoppage-time header earned Arsenal an unlikely 3-3 draw at Bournemouth after they had looked down and out when trailing 3-0 after 70 minutes of a rivetting Premier League clash on the south coast on Tuesday.
Arsene Wenger hailed Olivier Giroud's stunning strike against Crystal Palace as a work of art and one of the top five Arsenal goals in his 20-year reign.