The spokesman for the Hessian state government said on Friday that the fake bomb sent to the chancellery in Wiesbaden did not have any explosive material in it, but that authorities were taking the case "very seriously."
A group calling itself the "Morning Light Movement" claimed responsibility for the threat, saying it was a response to Koch's recent demands that those receiving Germany's Hartz IV welfare benefits should be pushed harder to work.
The group warned if Koch that if he repeated his remarks, a real bomb would be detonated "somewhere near your properties."
State authorities have launched an investigation, according to spokesman Dirk Metz.
The group behind the threat was unknown until last fall when it took responsibility for two arson attacks on banks in Frankfurt.
A conservative hard-liner, Koch has become a polarising figure in his state in recent years. Voters punished his Christian Democrats during an election in 2008 after he started a controversial campaign against young immigrants, but his image was first seriously tarnished for his involvement in a party slush fund scandal in 2000.