The Brazilian is being held by Munich police on suspicion of burning down his own house last week.
However, Rummenigge believes taking away Breno's freedom during the investigation into the fire, which completely destroyed the rented property in one of the city's most affluent districts, is an "exaggerated measure".
Having spoken with the 21-year-old's solicitor, he feels the player should be freed and allowed to get on with his life.
"I have spoken again to his solicitor, who has daily contact with him, and he says that Breno is not doing very well, which is understandable," said Rummenigge on Sky television.
"He is obviously psychologically very delicate. The solicitor has called for a meeting to discuss his custody terms and we hope that he will be released quickly because we believe it was an exaggerated measure to take him into custody.
"I believe it is important that the state prosecutors and also the judge show the necessary sensitivity and fairness in this issue.
"There are no risks of him trying to suppress evidence or fleeing."
Breno is reported to have been alone in the property when it went up in flames just after midnight on September 19.
He was taken into custody on Saturday after preliminary investigations carried out on the property suggested the fire may have been deliberate.