The 24-year-old was subjected to a verbal racist attack while training with his German league club on Sunday, when a group of between five and 10 fans in a crowd of at least 100 chanted anti-Semitic slogans.
They also gave the Nazi salute, which is banned in Germany.
"We are horrified by the anti-Semitic and racist acts aimed at Itay Shechter," said the Israeli embassy in a statement. "We have every confidence in the German authorities and are confident that the perpetrators of these acts will be brought before the courts as quickly as possible."
Shechter, who has played for Israel, is not believed to have seen the incident, but the club informed the police and issued an appeal for witnesses, while condemning the actions of the small group.
"Anti-Semitism and racism should not be allowed to have any place in football," said Wolfgang Niersbach, who is set to take over the DFB presidency on Friday.
"We must defend ourselves with all possible means at our disposal and we hope that the authorities pursue the case with all its consequences."
Shechter has so far scored three goals in 19 league appearances for Kaiserslautern, who are currently second from bottom of the league, but is currently injured.
Sunday's incident came the day after his team's 4-0 defeat by Mainz -- their fourth straight loss -- in which he did not play.
He has been left out of the Israel squad for their friendly international against Euro 2012 co-hosts Ukraine on Wednesday.