Third-tier Hansa said a flare was set off from the away end shortly after half-time, before the game was later suspended for 10 minutes.
Hertha Berlin added that the referee called both teams off the pitch for safety reasons in the 77th minute.
The Bundesliga side scored twice to win the game 2-0 after play resumed.
Players were forced to leave the pitch during Hertha Berlin's German Cup first round game at Hansa Rostock after fans let off flares and fireworks.