Enke out of Dortmund match
Enke could also miss Germany's top-of-the-table clash with Russia in a Group Four World Cup qualifier on October 10, having been picked to start in the remaining group matches.
Enke, who pulled out of Germany's squad before the qualifier against Azerbaijan last week with a mystery infection, has been doing individual training while doctors conduct further tests.
"Final results should not be expected before the end of the week," Hanover said in a statement.
"Until the diagnosis, Robert will only be participating in a light individual training. So he will not be available for the match against Dortmund," the club added.
Blood tests at a Hamburg institute specialising in tropical diseases have been negative for infectious illnesses.
Enke is competing with Tim Wiese, Rene Adler and Manuel Neuer for Germany's number one spot and national team coach Joachim Loew has said he would likely not play against Russia if he returned to action only days before that match.
Germany are top of Group Four a point ahead of Russia.