Brodsky, who was arrested in June at Poland's Warsaw airport on suspicion of obtaining a German passport under false pretences, was extradited to Germany on Thursday.
He now faces only those charges relating to passport fraud as that is the offence for which Poland agreed to extradite him.
But Rainer Wolf, the spokesman for the prosecution, cautioned that Brodsky could face spying charges if he leaves Germany and later returns.
Wolf said the most likely penalty option for passport fraud was a fine of some kind.
Brodsky is accused of illegally obtaining the German passport under the name Michael Bodenheimer, which was later found to have been used by a member of the hit-squad that killed Mahmoud al-Mabhouh earlier this year.
The squad, which Dubai police believe was from Mossad, the Israeli spy agency, was found to have used 26 doctored foreign passports, sparking a diplomatic fallout not only with Germany but also Australia, Britain, France and Ireland.
But Israel has denied any Mossad involvement in the assassination of al-Mabhouh, the founder of the military wing of Hamas, the Palestinian movement that controls the Gaza Strip.
In the wake of the alleged spy's arrest, Israel called on Poland to send Brodsky straight home rather than handing him over to Germany.