Harald Kleber - who is married to an Afghan woman and carries an Afghan passport - was kidnapped in mid-December in the western province of Herat.
The director of the Afghan foreign ministry branch in the province, Homayoun Kamgar, said intelligence reports indicated the hostage was ill.
"Based on information we have received, the abductors have demanded $50,000 from his family for his release," Kamgar told AFP.
Kleber, 42, a carpenter, had been kept "somewhere" between Herat and Farah province for the past three months, he said. "He is not in good health due to the severe cold winter and poor living conditions," he said.
The abductors had initially demanded $100,000 for his release but decreased the amount to $50,000, Kamgar said.
Four relatives of the German's Afghan wife were arrested but had been released on bail after investigations showed they might not be involved, he said.
Police spokesman for western Afghanistan, Abdul Rauf Ahmadi, said police were still trying to find the hostage.
"We are still investigating and trying to locate where he is kept and release him," he said.
Kleber worked for a humanitarian organization in Herat between 2003 and 2004 and then stayed in the country.
A German prosecutor said in December that an arrest warrant had been issued for him over allegations of computer fraud in his native country.