Bayern have won their opening five matches to sit two points clear at the top of the league ahead of Saturday's game against improving Werder Bremen, with champions Borussia Dortmund seven points adrift.
The situation was similar last season when, after six games, the difference between the two was eight points before Dortmund roared back for a successful title defence.
"I will keep both feet firmly on the ground and will not start flying," Rummenigge said. "We are on a roll, we are playing good football but there is no place for euphoria.
"The main aim is the Bundesliga title. There are another 29 match days and it is a long and potentially bumpy road, so we cannot repeat the mistakes of the past."
Bayern spent heavily in the off-season and have more depth in the squad following a string of transfers including central defender Dante, midfielder Javi Martinez and forwards Claudio Pizarro and Mario Mandzukic.
With winger Arjen Robben and Franck Ribery back fully fit and in fine form, last season's Champions League finalists are eager not to have another season without silverware.
"We were eight points clear last season and then we gifted the title away," Bayern captain Philipp Lahm told reporters. "This cannot happen this season again. We have been warned."
The prospect of hosting a fired-up Bayern, who have scored 17 goals and conceded two, should be daunting for Bremen's young squad.
"Bayern are the clear favourites and we can go into the game very relaxed. I am eager to see how our team will handle this situation," said Werder sporting director Klaus Allofs after his side came from a goal down to beat Freiburg 2-1 on Wednesday.
"We have to reduce our mistakes because Bayern will punish us," he said. Bremen are in seventh place on seven points.
Dortmund, in sixth on eight and looking for their first win in three games, host Borussia Monchengladbach. The champions squandered a two-goal lead on Tuesday to draw 3-3 with Eintracht Frankfurt.
Coach Jurgen Klopp will have forward Marco Reus fit after an ankle injury scare against Frankfurt.
Fellow Champions League competitors Schalke 04 travel to promoted Fortuna Dusseldorf, who have yet to lose this season and are in fifth place, for their game on Friday.
