Mario Rönsch, 35, who was arrested in Budapest in 2016 on a European arrest warrant, received a term of two years and 10 months.
Because he can still appeal the verdict, he was allowed to leave the court but will have to regularly report to police.
Rönsch in 2016 set up several websites labelled “Migrantenschreck” (Migrants' fright) on which he urged buyers to “arm themselves against refugees”.
He sold 167 of the permit-requiring firearms which fire high-velocity rubber bullets that can hurt or even kill, earning almost €100,000, which were confiscated.
Rönsch admitted to the internet sales but claimed ignorance he had broken German law and voiced no contrition or regret, the court found.
The judge pointed out that Rönsch had advertised the weapons as capable of “taking down asylum seekers”, a “seditious” sales pitch that took advantage of racist sentiments “in a particularly insidious way”.