Loew, captain Philipp Lahm and Polish-born Miroslav Klose and Lukas Podolski joined German FA officials as they crossed into the death camp through the infamous "Arbeit macht frei" (Work sets one free) gate.
Many of the 1.5 million, mostly Jewish, prisoners who later perished at the Nazi extermination facility crossed under the same sign during World War II.
Members of the footballing group did not speak to the media but in a note left in the museum's visitors book, they wrote: "For football too Auschwitz represents both a silent tribute and, above all, an obligation to speak.
"To speak about this endlessly sorrowful, hate-filled history and the warning it sends."
During a low profile visit, the players and officials, wearing dark coats that matched the chilly weather and their sombre expressions, toured the remains of the former Nazi camp including the gas chamber and wooden barracks that housed the inmates.
The group then passed by the railway platforms used to unload prisoners locked in cattle carriages and bound for almost-certain death to light 22 candles in honour of the main nationalities whose members perished there.
They also walked through a dedicated female part of the camp in Auschwitz II, or Birkenau, a larger extension of the main site added when the Nazi-sponsored Holocaust was in full swing.
The Auschwitz-Birkenau museum is located in the south of Poland, which will co-host along with Ukraine the Euro 2012 tournament that starts next Friday.
England, Netherlands and Italy, who will all train in the nearby city of Krakow, also plan to visit Auschwitz during their time in Poland.
Much of the Holocaust was perpetrated on Polish soil by its war-time Nazi occupiers, nearly wiping out its entire Jewish community of some 3.3 million people prior to 1939.
Poland has maintained some of the death camp facilities as a reminder of the atrocities perpetrated by the Nazis on its soil.
Earlier on Friday, Polish President Bronislaw Komorowski welcomed a letter from U.S. counterpart Barack Obama who expressed regret over using the phrase "Polish death camp" this week, which some Poles see as suggesting they were partially responsible for the crimes perpetrated by the Nazis.