The prosecutor's office in the northern city of Rostock confirmed on Thursday they had opened a probe against Michael Fischer on suspicion he was part of the attack on February 25.
Until recently, he was an official with the National Democratic Party of Germany (NPD), a neo-Nazi political party.
Drygalla, 23, left the Olympic village in London last week in the wake of media reports about her relationship with Fischer, who insists he has turned his back on the extreme right. He maintains contact with neo-Nazis.
The rower for her part has publicly said she rejects racism and extremism.
A spokeswoman for the prosecutor's office said the probe was linked to an incident in February in which up to 30 masked far-right militants rampaged during a memorial ceremony in Rostock for victims of a neo-Nazi cell accused of killing 10 people.
The attackers were armed with iron bars and wooden planks and a police officer was injured in the melee.
"It is suspected that Mr Fischer was present in the group," the spokeswoman said, adding that another 12 people were under investigation in connection with the incident and could face charges of "aggravated disturbance of the peace".
Fischer, a former NPD candidate for the regional parliament and an active member of the local far-right group National Socialist Rostock, resigned from the party in May.
Drygalla was a member of the German eight but the team was eliminated in the repechage stage.
Fischer's relationship with the far-right was long known, according to German media, as was the fact that Drygalla resigned from the police service last year because of her ties to him.
The case has sparked a debate in Germany as to whether Drygalla should be judged based on the views of her boyfriend, with both the head of the German Olympic delegation and a government minister coming to her defence.