The pair, a man and a woman in their early 20s, were picked up after a series of raids on houses in Diepenbeek and Ostend, prosecutors said.
One house contained large quantities of Nazi memorabilia and flags, they added.
The allegations against the two include "recruiting people with the aim of committing terrorist crimes".
They are also suspected of "preparing for the commission of terrorist acts".
The Belgian raids were part of a Europe-wide operation against right-wing terrorism that also included raids in Croatia, Germany, Lithuania, Romania and Italy, according to the EU's crime agency Europol.
In all,five people were apprehended and seven others interrogatedacross the different countries, it said.
The two people taken into custody by Belgian police have been identified as Daan C, born in 2000, and Kayley W, born in 2002.
Daan C was arrested pending further investigation, while Kayley W was released after questioning.
"Both persons are suspected of participating in the activities of a terrorist group, with Daan C also as a leader," said a statement from the federal prosecutor.
"There are indications that the suspects were active on several encrypted extreme-right platforms, urging people to commit terrorist acts, recruiting new members and sharing information on how to use 3D-printed firearms," the statement went on.
"They were also found in possession of materials that could be used to produce home-made bombs and petrol bombs."
In addition, prosecutors said some members of the online groups had written a manifesto and there were indications they had weapons at their disposal.
"Despite the young age of some of the suspects, indicators showed that there was an increased risk that some of them would take action soon," Europol said.
Anti-terrorism police in Belgium have detained two suspected members of a far-right group accused of plotting bomb attacks and inciting violence.