Scudamore and the Premier League have encountered a growing tide of criticism with a number of England women internationals calling for action against the league's chief over sexist emails that he sent to a lawyer friend.
Now Rabbatts, who also chairs the FA's inclusion advisory board (IAB) which is meeting on Tuesday to discuss the case, has issued a statement saying there is a lack of good governance in the league and a culture at the top that "demeans women" and discourages them from being part of football administration.
Rabbatts said in a statement released to Press Association Sport: "No-one can doubt the tremendous achievements of the Premier League in creating one of the world's great footballing competitions. But with that success and the massive public interest it generates comes the obligation to behave responsibly and have in place proper lines of accountability and good governance.
"Sadly recent events appear to show that these things are currently lacking in the administration of the Premier League and indeed there is growing evidence of a closed culture of sexism, symbolised in the email exchanges which have been made public.
"It is increasingly clear that steps are needed as a matter of urgency to review governance at the Premier League with a view to improving accountability and tackling head on a culture that demeans women and seems to discourage their involvement in the game's administration.
"These challenges go beyond the current situation of chief executive Richard Scudamore. However, if the League are to move forward in a positive way then he and they should give serious consideration to his position in the coming days."
Rabbatts said it was important for the women's game that changes were made.
She added: "I personally hope that progress can be made on all of these fronts so that we can feel confident that the leaders of football are accountable for their actions and support a culture that genuinely welcomes the participation of women and girls in our national game."
Sponsor Barclays has expressed its disappointment to the Premier League, which has raised the stakes ahead of a meeting of the league's audit and remuneration committee, chaired by Chelsea chairman Bruce Buck, on Monday to discuss the case.
Buck's involvement has also raised questions, as he is known to be a friend and shooting partner of Scudamore's. The Premier League is reported to have brought in Milltown Partners public relations agency to advise it on handling the crisis - and it also reported that the PR company works for Chelsea too.
Meanwhile, England women internationals have added their voice to the criticism.
Everton women's goalkeeper Rachel Brown-Finnis said the emails were an "insult to all women" and that Scudamore should be sanctioned, while former England captain Casey Stoney said his position was now "difficult".
The group Women In Football has written to all 20 Premier League clubs and main sponsors asking for an "independent review" of the league's practices.
Stoney said in the Daily Telegraph: "We are trying to get to a world without discrimination and to have somebody in such a high position in football making derogatory comments about females is not acceptable.
"How would he feel if these comments were written about his daughters?
"It is up to the powers that be whether he stays on but talking about women in such a derogatory way makes his position very difficult. Whether it's a private email or not, he has written them and he has only apologised because he has been caught."
Brown-Finnis told BBC Sport: "It's not just about women who are involved in football, it was an insult to all women.
"However jokey he was trying to be with that, it's just totally unacceptable in this day and age.
"It's zero defence for me. Private emails when you are the head of the Premier League don't really exist.
"Is a sorry enough? Probably not, but I do think the way to move forward is for the Premier League to follow its protocols just like it would with other employees and I'm sure it has policies which would sanction him appropriately for his misconduct."
The emails referred to women in derogatory terms, contained sexual innuendoes, and made jokes about "female irrationality".
After the story broke in the Sunday Mirror, Scudamore issued a statement apologising for the emails, which were sent from his Premier League email account and seen by a former temporary PA who leaked them to the newspaper.
- Sports & Recreation
- Premier League
- Richard Scudamore