National Liberation Army (ELN) guerrillas identified their captives as "Messrs. Breur Uwe and Breuer Gunther Otto, of alleged German nationality," in a statement on its website, www.eln-voces.com.
The men were captured in the Catatumbo region, in northeastern Colombia near the border with Venezuela, the group said.
The rebels described their hostages as "intelligence agents," saying that the pair "have been unable explain their presence in this region in the weeks since they were detained."
"To date, no group or person has lodged any kind of complaint regarding their disappearance," ELN noted, adding that "spies are not protected under international humanitarian law."
President Juan Manuel Santos quickly called on the rebels to release the Germans, and held the ELN responsible for their safety. Santos ridiculed the idea that the men could be spies.
"Who could possibly believe that two Germans were spying here in Colombia?" Santos asked. "That's an excuse that no one in their right mind would accept or understand."
The Germany embassy in Bogota said that they would not comment "out of respect for the hostages and their families."
The ELN, is Colombia's second largest guerrilla group after the better-known Revolutionary Armed Forces of Colombia (FARC). Founded four decades ago, it has around 2,500 fighters and is active in northeastern Colombia.
Last month the group claimed to have kidnapped six mining company employees, including a Canadian and two Peruvians, in northern Colombia, claiming the move was aimed at defending the region's natural resources.
The guerrillas warned the army not to try a military rescue operation and Santos pledged there would be "no operation putting the hostages' lives in danger," but said authorities know where the six hostages are being held.
In recent months, the ELN has said it was ready to hold peace talks with the government, saying it wanted to join in on negotiations between the Santos administration and FARC currently underway in Havana.