The German team said Steffen was diagnosed with knee ligament damage following an examination on Monday.
Steffen started Fortuna's first 17 Bundesliga games this season on loan from Manchester City. But he hasn't played since December because of a problem with a tendon connected to his kneecap.
Steffen missed eight league games before the Bundesliga was suspended last month because of the coronavirus pandemic.
Fortuna sporting director Lutz Pfannenstiel said the new injury has "nothing to do" with Steffen's previous problems.
"With Zack Steffen it is particularly annoying. We had only just got a grip on his patellar tendon problems thanks to hard work," Pfannenstiel said.
German players have returned to limited training in small groups as the league aims to return to competition next month. That depends, however, on approval from numerous political figures at federal and state level.
Fortuna, which is in 16th place in the 18-team Bundesliga, also announced that midfielder Adam Bodzek has a thigh muscle tear.