Olic traded blows with Hoffenheim midfielder Carlos Eduardo near the end of a match played in La Manga on January 14 during the German league's winter break.
The German Football Association (DFB) said on Friday that both players would be suspended for the next two competitive matches as well as three friendlies.
Olic is set to join Bayern Munich at the end of the season after agreeing a three-year deal with the German champions.
As well as missing the January 30 home game against his future employers, the Croatian forward will miss Hamburg's trip to Karlsruhe.
Eduardo's suspension could prove costly for shock league leaders Hoffenheim as they restart their Bundesliga campaign away to Energie Cottbus and home to Borussia Moenchengladbach.
Hoffenheim were already without the league's top scorer Vedad Ibisevic, who is expected to miss the remainder of the season after tearing a cruciate ligament in the La Manga friendly.
With fellow Hoffenheim striker Chinedu Obasi struggling to recover from a thigh muscle injury, Eduardo was a possible replacement upfront.
Hoffenheim, bidding to become the first team to win the Bundesliga in their maiden season in the top division, lead second-placed Bayern only on goal difference.
Hamburg are just two points further back in fourth place, level on points with third-placed Hertha Berlin.
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
