He had been feeling unwell for more than two weeks and pulled out of the September 9 World Cup qualifier against Azerbaijan in Hanover, when Bayer Leverkusen's Rene Adler took his place.
A series of tests had initially failed to find the cause of Enke's illness.
'The time of uncertainty was very nerve-wracking,' Enke said last week.
'I hope following this diagnosis that I will be fit again soon and can return to team training.'
Germany lead Group 4 on 22 points, one ahead of Russia before their meeting in Moscow on October 10. The Germans take on Finland, who can no longer qualify, four days later in their final group match.