Franca, who joined the Bundesliga outfit in January from Brazilian side Coritiba, is expected to miss several months while he recovers from the condition.
"I am so sorry for Franca," Hannover sports director Joerg Schmadtke told the club's website. "The most important thing now is that he becomes healthy again. We wish him all the best for his recovery and know that he is in the best hands."
The regional tuberculosis advisory agency chief Helga Heykes-Uden said that it is unlikely that the source of the infection is in Hannover, as it takes at least four months for the disease to become active.