The broadcaster promised to ponder the concerns raised following Barnett’s interview with the first woman to head the Muslim Council of Britain.
More than 100 prominent personalities signed an open letter on Radio 4 about Zara Mohammed’s “abuse”.
The show said it would “think hard” about how Muslim women should be reflected.
Director General Tim Davie said he agreed with the program’s stance and that the BBC had “a responsibility to investigate and debate issues in all communities”.
The open letter, released on Wednesday, was signed by a number of politicians, writers, scholars and other public figures.
It said Barnett had “shown an intention to augment harmful and adverse tropes against Islam and Muslim women” and that the company had to “deal with and represent Muslim women”.
In the letter, the host was asked particularly about “persistent” questions about how many female imams there are in Britain.
“Despite Muhammad’s repeated claims that religious jurisdiction was not within her role as leader of a civil society organization, Barnett asked the question about female imams four times, interrupting Muhammad’s response each time,” it said.
The interview “reflected the style and tone of an accountability interview with a politician, rather than being authentic about and delving into what this represents for British Muslim women,” the letter added.
“Deepen our commitment”
In a statement on Friday, the program said: “While we appreciate that people can sometimes have very different reactions to our live interviews and discussions, we feel it is legitimate for the program to attempt to address some of the problems examine faced Muslims in the UK.
“However, Woman’s Hour has always been a program that listens to feedback and learns from the responses we receive. We will ponder the issues and concerns that you raise in this open letter.
“We always try to reflect and reflect on the experiences and problems that affect Muslim women, and how we do them, and we will continue to do so.
“We pledge to get back on the air soon and to deepen our commitment to the issues that matter most to Muslim women and to be represented during Women’s Hour as part of the BBC’s plans to more closely reflect the society we serve . “
The open letter said part of the problem was that Muslim voices were “underrepresented at all levels” within the BBC.
Mr Davie acknowledged that the BBC’s Muslim staffing rate is below the national average, but added, “It’s not as low as you suggest.”
He said: “Improving the representation of our employees is a top priority for me and my management team.”
He invited the writers of the letter to “meet with some senior colleagues from the BBC to discuss the issues you raise in your letter” in order to understand the BBC’s plans, “to be represented in our programs and in ours To improve teams ”.