The sign, which means "Work Will Set You Free", has become a symbol of the horror of the camp where about 1.1 million mainly Jewish prisoners died during World War II, most in the notorious gas chambers.
An Israeli deputy prime minister called the theft "an abominable act" while a leading Israeli holocaust memorial group said it was "a declaration of war."
Auschwitz-Birkenau Museum spokesman Jaroslaw Mensfelt told AFP that thieves carried out an expert operation to take the metal sign just before dawn on Friday. "It's a profanation of the place where more than a million people were murdered. It's shameful," he said. The five-metre (16-foot) long sign was forged by prisoners on the orders of the Nazis, who set up the camp after invading Poland in 1939. It was not hard to unhook from above the entrance gate "but you needed to know how," Mensfelt said.
A police dog team tracked the thieves while detectives combed through video surveillance footage from the site and neighbouring areas.
Poland's ex-president Lech Walesa called the theft "unthinkable". "I hope this turns out to be a sick joke by scrap-metal thieves who didn't know what they were doing," the Nobel prize winner told the TVN24 news channel.
In Israel, Avner Shalev, director of the Yad Vashem Holocaust memorial said "this act constitutes a true declaration of war." "We don't know the identity of the perpetrators but I assume they are neo-Nazis," Shalev said in a statement."I am certain the Polish government will do everything possible to track down those criminals and put them on trial," he said.