We are ordering the recall," a spokesman for the motor transport authority said, confirming a report by German daily Bild.
Volkswagen admitted last month it had installed software in diesel vehicles to deceive U.S. regulators about the true level of their toxic emissions.
It has said it aims to start a recall of affected cars in January and complete fixes by the end of next year, but Bild said the KBA had rejected the idea that owners could voluntarily bring in their vehicles.
Volkswagen said it had not received any orders from the KBA.
The carmaker is under pressure to identify those responsible for the wrongdoing and fix up to 11 million affected diesel vehicles worldwide. It has been criticised by politicians, investors and consumers for the time it is taking to produce answers.
The KBA and other European national authorities are due to provide an update to the European Commission in Brussels later on Thursday on investigations of the emissions scandal in their respective markets.
Also, Germany's transport ministry, which has in the past said about 2.8 million cars in Germany were affected, said Transport Minister Alexander Dobrindt would make a statement on Volkswagen at 11 a.m. (0900 GMT).
