"Such incident -- an offense against the Memorial Site -- is, above all, an outrageous attack on the symbol of one of the greatest tragedies in human history and an extremely painful blow to the memory of all the victims of the German Nazi Auschwitz-Birkenau camp," the statement read.
"We hope that the person or persons who committed this outrageous act will be found and punished," it continued, alongside an appeal for eyewitnesses to share information.
Auschwitz-Birkenau, established in Nazi-occupied Poland, was the largest concentration camp run by Hitler's regime. More than 1.1 million men, women and children were systematically murdered there, many in the camp's gas chambers. Some 6 million Jews were killed in the Holocaust.
The museum said security at the 170-hectare site is "constantly" being expanded but it is financed by the museum's budget, which has been hit by the coronavirus pandemic.
The number of anti-Semitic incidents in Germany has been growing steadily in recent years, Deutsche Welle reported in February.
There were at least 2,275 anti-Semitic crimes in the 12 months to the end of January 2021, some 55 of which were violent, it reported.