Manfred Hämmerle, chairman of the party in Hückelhoven near the Dutch border, has been accused of illegally selling a submachine gun, and possibly a Kalashnikov AK47 as well as an Uzi machine gun.
Der Spiegel magazine, which reported the story on Saturday, said he could face at least a year in prison if convicted of charges of breaking the military weapons control laws.
Hämmerle, 44, reportedly a keen sports marksman, came to the attention of prosecutors after an optician was murdered, shot to death with his own English Sten MkII submachine gun.
Detectives discovered he had bought the weapon from Hämmerle, who is also accused of illegally supplying several other powerful weapons.
A conviction would be doubly embarrassing for The Left, or Die Linke in German, because the party is avowedly pacifist, and has been campaigning for a ban on weapons being kept in private homes.
“That is a serious break with the anti-war policy of our party,” Ulla Jelpke, MP for The Left said with reference to the traffic in weapons.
“My client did not exactly know the legal situation,” said Hämmerle's lawyer Heribert Kayenburg.