The Federal Criminal Police Office (BKA) registers around 200 crimes per week in Germany in connection with the war in Ukraine, local media reported on Wednesday.
The crimes were directed "mostly against members of our society of Russian origin, but also against members of Ukrainian origin," BKA President Holger Muench told Tagesspiegel, a Berlin-based daily.
These are primarily crimes such as threats, insults, and property damage, he said.
It has been almost two months since Russia launched a war on Ukraine.
German Interior Minister Nancy Faeser warned earlier this month that the war could spill over in German society with unpredictable consequences.
"This conflict should not be allowed to creep into our society," Faeser stressed.
"We have to remind people that this is Putin's criminal war. It is not the war of people with Russian roots who live here in Germany," she added.
German police are also investigating displays of support for the Russian war on Ukraine.
Over 140 incidents of alleged endorsement of the war are part of the probe by authorities. Many involve the use of the controversial "Z" symbol which has been associated with Russia's war after many of the vehicles that Russian forces drove into Ukraine had the letter painted on their side.
Several German states have branded the use of the symbol as unlawful support for the war.
Meanwhile, German federal police have reported more than 350,000 refugees in Germany since the war began on Feb. 24. It is believed that the actual number is significantly higher.