On one of the pictures, a soldier is seen holding the skull next to his exposed penis, on another - soldiers pose with the skull on their jeep.
German chancellor Angela Merkel expressed disgust at the photos and said there would be full investigation.
Two possible suspects have already been identified and are being questioned, said army chief of staff General Wolfgang Schneiderhan.
One of suspects was still with the armed forces and the other had left the army, the general said.
"We all saw pictures today that are shocking, that are repugnant and that can be excused by nothing," Chancellor Merkel said.
"The government will investigate the soldiers who played a role and act with full severity," she added.
German Defence Minister Franz Josef Jung pledged "disciplinary or even criminal measures" for those involved, if the story was confirmed.
"Anyone who behaves this way has no place in the Bundeswehr [German military]," he added.
The story was given wide coverage on German television on Wednesday.
"We can't use such people in our army," Bernhard Gertz, head of the main organisation representing German troops, said on ARD television channel.
"We must investigate exactly how such degeneration and misbehaviour can happen despite good training and good supervision," he added.
The Bild newspaper did not say how it had obtained the photographs, nor gave any proof of their authenticity.
It is not clear where the skull in the pictures came from, the newspaper admitted, adding that according to a military source it could have been taken from a mass grave.
Germany has about 2,800 troops stationed in Afghanistan within Nato's International Security Assistance Force (Isaf).
Unlike British, American and Canadian troops, who are fighting the Taleban in the south, the Germans are based in the relative calm of the capital Kabul and in the north of the country.
Last month, the Bundestag, the lower house of the German parliament, voted to extend the mission of the German forces in Afghanistan until October next year because of the worsening security situation there.
The scandal broke hours before the German cabinet was due to discuss Germany's continued involvement in Afghanistan and coincided with the defence ministry's first policy manifesto since 1994. Jung used the manifesto to state Germany's readiness to take on more international peacekeeping missions.
"It is clear that such behaviour cannot be tolerated from German soldiers. It runs counter to the values and codes of conduct we try to instill in our soldiers," Jung said.
The state prosecutor's office in Potsdam, outside Berlin, has launched a criminal investigation into the affair.
Germany is the second biggest supplier of peacekeepers to Afghanistan and holds the command of Isaf in the north of the country. About 2,750 Germans are serving with the force.
The Bundestag, or lower house of the German parliament, voted last month to extend their mandate in Afghanistan until October 2007.
Source: BBC and AgenciesGüncelleme Tarihi: 20 Eylül 2018, 18:16