Padlo also said that the iron sign, which spanned a gate at the main entrance to the former Nazi death camp in southern Poland, was removed by being unscrewed on one side and pulled off on the other.
Police deployed 50 investigators and a search dog to the Auschwitz grounds, where barracks, watchtowers and ruins of gas chambers still stand as testament to the atrocities inflicted by Nazi Germany.
Police were reviewing footage from Auschwitz's surveillance cameras to see if the theft was recorded.
Auschwitz museum spokesman Jaroslaw Mensfelt said the thieves carried the sign 300 meters (yards) to an opening in a barbed-wire gap in a concrete wall. That opening had been left intentionally to preserve a poplar tree dating back to the time of the war.
The sniffer dog led police to a spot outside the wall where the sign left an imprint in freshly fallen snow, then to a roadside where the sign appeared to have been loaded onto a getaway vehicle.
An exact replica of the sign, produced when the original received restoration work years ago, was quickly hung in its place.
Padlo said police were offering a 5,000-zloty ($1,700) reward for public tipoffs about the thieves.
Reaction from Israel to the incident was swift, with Diaspora Affairs Minister Yuli Edelstein (Likud) referring to the theft as a "critical failure of the Polish police."
Edelstein also said that "we are in a period in which anti-Semitic acts are on the rise and there is a tangible fear for the safety of Diaspora Jews."
"The anti-Semites and Holocaust deniers have no red lines and are now trying, to no avail, to reach their goal through the removal of Holocaust symbols," said Edelstein.
Polish Ambassador to Israel Anyeshka Mishevska told Israel Radio that the theft wasn't simple vandalism, but rather a well planned act.
She said that the thieves removed the sign, destroyed it and disappeared.
Mishevska claimed that the thieves capitalized on a six-minute slot between guard shifts when they knew the security post would not be manned. The Polish envoy stressed that the act wasn't just an anti-Semitic crime, but "a crime aimed against the memory of the entire Holocaust."
Acting museum curator Christina Alexi told the radio station that "we're all shocked."
"For years we have kept a replacement sign for the original, and immediately upon hearing of the theft we put it up," she added.
Noah Flug chairman of The Center of Organizations of Holocaust Survivors in Israel and president of the International Auschwitz Committee called on the Polish police and government to "make every concerted effort to track down the perpetrators and bring them to justice."
Flug said that the sign is "an item of both important symbolic and historical value."
Yad Vashem chairman Avner Shalev said he was "shocked" to learn of the theft of the sign, "which has come to symbolize the murder of 6 million Jews during the Holocaust."
"While we don't yet know exactly who stole the sign, the theft of such a symbolic object is an attack on the memory of the Holocaust, and an escalation from those elements that would like to return us to darker days," he said in a statement. "I call on all enlightened forces in the world - who fight against anti-Semitism, racism, xenophobia and the hatred of the other, to join together to combat these trends."
Also speaking to Israel Radio, Tel Aviv-Yaffo Chief Rabbi Yisrael Meir Lau, a Holocaust survivor and chairman of the Yad Vashem Council, called the theft "frightening and painful." He said the sign was the one of the firmest proofs of the Holocaust, and was a huge contribution to the perpetuation of the victims' memory.
On Thursday, Germany announced that it was donating €60 million ($87 million) to a new endowment for Auschwitz-Birkenau to preserve barracks, gas chambers and other evidence of Nazi crimes at the former death camp.
Lau said the proximately of the theft to Thursday's announcement and to next month's ceremony at Auschwitz marking 65 years since the camp's liberation was no coincidence.
"This sign was an expression of what happened there and they (the thieves) want to forget and cause others to forget," he said.
Holocaust Educational Trust Chief Executive Karen Pollock also expressed her fury at the theft.
"The Nazi death camp Auschwitz-Birkenau stands as a universal symbol of the Holocaust and for millions of victims, the sign represented the cynical cruelty of Nazi rule," she said in a statement. "We are disgusted by this appalling act of vandalism and the gross disregard it shows to all Holocaust survivors and the families of those who lost loved ones there."
Poland's chief rabbi, Michael Schudrich, said he had trouble imagining who would steal the sign.
"If they are pranksters, they'd have to be sick pranksters, or someone with a political agenda. But whoever has done it has desecrated world memory," Schudrich said.
"Auschwitz has to stand intact because without it, we are without the world's greatest reminder - physical reminder - of what we are capable of doing to each other," he said.
In Brussels, European Parliament president Jerzy Buzek appealed to the thieves to return the sign.
"Give it back out of respect for the suffering of over a million victims, murdered in this Nazi camp, the biggest cemetery of humankind," Buzek said.