Guards at the Polish site first noticed that the gate, which translates to “Work Shall Set You Free,” was missing and called police around 3:30 am on Friday morning, Jaroslaw Mensfelt said.
There is no trace of the perpetrators, he added, explaining that they had apparently been well prepared.
“Whoever did this knew exactly what they wanted,” Mensfelt said.
Until the original can be found, officials at the camp have replaced it with a copy that was made during renovations.
Polish politician Bogdan Borusewicz told a radio broadcaster in the country that the theft “regrettable and embarrassing.”
The cynical statement on the gate has come to symbolise the tragic fate of the 1.1 million Jews murdered at Auschwitz during the Second World War. It was crafted by Polish prisoners at the camp in 1940 under order of their German captors. The phrase was also used by the Nazis at other concentration camps.
German Foreign Minister Guido Westerwelle blasted the theft of sign at the former death camp as a "shameful act that must be punished."
"We assume that the justice authorities will do everything in their power to catch the culprits and impose a just sentence," he said after talks with his Polish counterpart Radoslaw Sikorski.
Sikorski said he was stunned by the crime. "I am at a loss for words," he told reporters. "We hope the culprits will be arrested soon."
The German Jewish community also expressed disgust.
"This is shocking and hurtful and dreadful and tasteless," Dieter Graumann, vice chairman of the Central Council of Jews in Germany, told news agency AFP. "For all survivors and for survivors' descendants and for everyone this is a great hurt and a shock."