Senegal international Diouf, who joined the club from Manchester United in January, tore his ligaments after twisting his ankle early in the second half but played on to score the equaliser before hobbling off.
Seventh-placed Hanover travel to Werder Bremen on Sunday.
Borussia Moenchengladbach winger Patrick Herrmann returned to individual training on Thursday after breaking his collar bone in mid-February.
The 21-year-old, who had an outside chance of making the Germany squad for Euro 2012 before his injury, said he could not train with his team mates until the bone had completely mended.
He will not be available for Gladbach's match at home to Freiburg on Saturday.