The status should make it easier for authorities to use secret methods to monitor the party for example by recruiting confidential informants and intercepting communications.
The AfD did not immediately respond to a request for comment.
The stigma as well as restrictions on civil service employment could also hamper its ability to attract members.
"The ethnicity- and ancestry-based conception of the people that predominates within the party is not compatible with the free democratic order," the domestic intelligence agency said in a statement.
"It aims to exclude certain population groups from equal participation in society, to subject them to treatment that violates the constitution, and thereby assign them a legally subordinate status."
The AfD does not consider German citizens of immigrant background from predominantly Muslim countries as equal members of the German people, it added.
This approach led to individuals and groups being "defamed and vilified", stirring up "irrational fears and hostility toward them," it added.
Friday's decision comes days before conservative leader Friedrich Merz is due to be sworn in as Germany's new chancellor and amid a heated debate over how to deal with the AfD in the new parliament.
The party won a record number of seats which theoretically entitles it to chair several key parliamentary committees although it would still need the backing of other parties.
Reacting to the designation, Interior Minister Nancy Faeser said the AfD pursues a proven campaign against the free democratic order.
"The AfD represents an ethnic concept that discriminates against entire population groups and treats citizens with a history of migration as second-class Germans," Faeser said in a statement.
"Their ethnic attitude is reflected in racist statements, especially against immigrants and Muslims," she added.
Analysts said the decision risks further fuelling support for the AfD and its narrative that it is being sidelined by a "cartel" of established parties. The party has topped several polls in recent weeks.
Certain factions of the AfD such as its youth wing had already been classified extremist, while the party at large was classified a suspected extremist case in 2021.
