The move follows a probe by the Chief Commission for the Prosecution of Crimes Against the Polish Nation, the investigative arm of the Warsaw-based Institute of National Remembrance (IPN), the niezalezna.pl website reported.
It said the history institute posted the news on its website on Wednesday.
The investigation was launched by an IPN prosecutor ex officio and is being conducted by the institute's Poznań branch, according to niezalezna.pl.
The news website quoted IPN prosecutor Robert Janicki as saying that the former East Germany security-service officer in question, a German citizen identified as Manfred N., is suspected of shooting a Polish man, named only as Czesław K., in the back and killing him more than 47 years ago.
The fatal shot was fired on March 29, 1974 on East Berlin's railway border crossing of Friedrichstrasse and the Stasi operative is believed to have been acting to prevent the victim from crossing the state border between East Germany and West Berlin, niezalezna.pl reported.
Earlier that day, Czesław K. visited then-communist Poland's embassy in East Berlin, claiming he had explosive material and threatening to set it off, unless he was allowed to cross into West Berlin, according to niezalezna.pl.
Polish communist officials sent word to Stasi, which decided the man must not be allowed to leave their country, even if that required the use of firearms.
However, Stasi operatives first made a show of granting Czesław K. the documents necessary for crossing the border, then drove him to Friedrichstrasse and arranged a mock "clearance" after which he was permitted to head towards West Berlin, niezalezna.pl said.
"As Czesław K. set off in the direction of the subway tunnel, a plain-clothes Stasi official, Manfred N., fired a gunshot in the victim's back from a distance of around two metres," the IPN said in a statement.
Seriously injured, Czesław K. was taken to hospital, where he died from the wounds, the IPN added.
In its official report, the Stasi claimed Czesław K. had brandished a gun which he was pointing at the border guards, one of whom shot at "the assailant" to "protect the life and health of those in danger," niezalezna.pl said.
The IPN noted that the operatives involved in "preventing the terrorist attack," as the incident was officially termed, received high-level state decorations.
Manfred N. himself was awarded the "Bronze Order of Merit in Fighting for the People and Motherland," according to the IPN statement.
The IPN said its probe "shows unequivocally" that the Stasi set a trap for the Polish man to stop him from crossing the border "at all cost, in violation of elementary human rights and in the name of implementing the political doctrine of a totalitarian state."
The history institute's Janicki said it happened despite the fact that Czesław K. presented "no threat whatsoever" and did not, in fact, "possess any explosive material."
"It was essentially an extrajudicial execution," Janicki added, according to niezalezna.pl.