In the 2017 election, AFD became Germany's third largest party, and is today the largest of four opposition parties.
The security service Bundesamt für Verfassungsschutz, BFV, has now ruled that the right-wing nationalist party may pose a threat to the free democratic system, which according to the German constitution gives the intelligence service special rights to put the party under surveillance - with certain restrictions.
It reports the newspaper Der Spiegel and several other media.
The decision must have been made last week, and is based on a 1,000-page report.
Among other things, it will contain hundreds of speeches and statements from AFD members at various levels within the party who are alleged to be contrary to the free democratic basic order, writes Der Spiegel.
"Fully motivated"
AFD leaders and parliamentarians Alexander Gauland and Alice Weidel say it is "completely unjustified and baseless", and says according to the AP that it is not a coincidence that the information was leaked to the press the same year as the parliamentary elections.
One of the main reasons for the new classification is stated to be the "Wing", a right-wing extremist, now disbanded branch of the party, which is still considered to have great influence over the party.
AFD is already under surveillance in the East German states of Brandenburg, Saxony-Anhalt, Thuringia and Saxony.
The youth union is also monitored.
Germany goes to the polls on September 26 this year.