The wrought iron sign, whose words mean “Work Sets You Free”, was unscrewed and pulled down from its position above the gate in the early hours of Friday.
Polish authorities denounced the theft, while Israel’s Holocaust museum branded it an “act of war”.
More than a million people – 90% of them Jews – were murdered by the Nazis at Auschwitz during World War II.
Investigators say at least two people would have been needed to steal the five-metre-long (16ft), 40kg (90lb) sign.
The theft occurred between 0330 and 0500 local time on Friday, police spokeswoman Katarzyna Padlo told AP news agency.
Jarek Mensfelt, from the Auschwitz-Birkenau Museum, told the BBC: “It is more than just stealing something. It is a desecration.