Verena Bahlsen, who owns a quarter of the company, said she “deeply regrets” comments she made about people forced into working at the biscuit factory during the Second World War under Adolf Hitler's Nazi regime.
“It was a mistake to amplify this debate with thoughtless responses. I apologize for that,” she said in a statement on the Bahlsen family's website.
“Nothing could be further from my mind than to downplay national socialism or its consequences.”
The 26-year-old had dived headlong into controversy first with her unashamed claim of being a capitalist who “wants to make money and buy yachts with my dividends”.
As critics reminded her on Twitter that her company profited from forced labourers during Adolf Hitler's Nazi regime, she hit back, telling newspaper Bild that “we paid forced labourers as much as Germans and treated them well”.
Her comments drew a furious outcry from politicians and historians alike.
The Nazi Forced Labour Documentation Centre, based in Berlin, said her case illustrated a lack of understanding about the plight of those made to work against their will by Hitler's regime.
On social media, there were calls to boycott Bahlsen's products, while others had urged the wealthy heiress to do a year of civic service to gain a better understanding of social realities.
“I also recognize that I need to learn more about the history of the company whose name I carry,” added a contrite Bahlsen in her statement.
“As the next generation, we have the responsibility for our history.
“I expressly apologize to all whose feelings I hurt.”
Founded by Verena Bahlsen's great grandfather at the end of the 19th century, the biscuit company employed around 200 forced labourers, mostly women, between 1943 and 1945.
Claims were made against Bahlsen by victims after the war, but they were rejected because of the statute of limitations.