The 34-year-old, who has scored 65 times for Germany in 125 appearances, won the prize after informing the referee a goal he had scored for Lazio against Napoli in Serie A at the end of September had hit his hand first.
After Klose's confession, the referee cancelled the goal as Lazio went on to lose the match 3-0 at Napoli. The German was praised by his opponents on the pitch and later by the Italian media for his honesty.
"I admitted it had and, for me, that was the obvious thing to do.There are so many young people who sit in front of the television, that we should set a good example."
Klose also won a similar award in 2005 when playing for Werder Bremen in a Bundesliga match against Bielefeld. After Bremen were awarded a penalty, Klose told the referee that the Bielefeld goalkeeper had the ball first before the striker fell in the area.
The referee reversed his penalty decision and also cancelled the yellow card shown to the goalkeeper.