Helen Grant held talks with Dyke on Monday after stinging criticism of the all-white and all-male make-up of the commission from FA board member Heather Rabbatts at the weekend.
That row was swiftly followed by Dyke appointing Rio Ferdinand and Roy Hodgson to the commission which will aim to find ways to make the England team more successful - but all 10 members are men.
Grant, who is also equalities minister, said Dyke had told her there could be more appointments made.
Asked if she would like to see a woman appointed, she said: "I think all governing bodies and commissions of this nature should seek to reflect the make-up of the society that it purports to represent and I know the contribution that women could make.
"I have met many fantastic women in my days as both a lawyer and as a politician and we will have to see what will happen."
She added: "I spoke to Greg on Monday and he has said he hasn't finalised the make-up of the commission.
"I have made my views very clear and I am very, very pleased to hear about Rio and I think his appointment will be a very good thing.
"The make-up of the commission isn't finished it, it hasn't be finalised and what we need to do is give Greg Dyke a bit of space now to work out what he needs to do."
Dyke's commission ran into trouble almost from the outset after the Premier League clubs decided that although they would contribute they did not want to have a representative on the body.
The FA chairman has described that position as "a shame" but Premier League chief executive Richard Scudamore defended the clubs and said they wanted the same outcome as Dyke.
Scudamore said: "Greg Dyke has come in and clearly is a very capable man with huge energy and huge passion and he has quite rightly made his number one priority a more successful England team.
"There is no argument from us. Look at the EPPP [academy programme], the first line it says is to produce more and better home-grown talent. There is nothing incompatible with what he is saying.
"Our 20 clubs are saying 'come and talk to us, we have got the expertise, we know what is going on, we have some fantastic people at the leading edge of how you develop young players'.
"We are your biggest allies in making this happen on a bigger, wider, better scale.
"The 20 clubs sat round and decided they all wanted to be part of it but they don't want a named person on it."
FA general secretary Alex Horne confirmed more members could be added to the commission and denied it was "a shambles".
He said: "I dispute that, I don't buy that it's any less credible or laudable than it was when we set out.
"The commission haven't even met yet or seen the terms of reference so of course the commission's make-up could change.
"Remember the objectives - the commission's aim is to look at pathways for talented young players eligible for playing for England and where they are playing their club football.
"The board are examining the detailed scope, timeline and terms of reference for the commission and it's vitally important we get the board to sign off on that as this is an FA board-owned commission, they are empowering Greg to get on with it.
"This will be one of the most inclusive consultations we have ever undertaken, we will be seeking input from all aspects of football and not only in England but overseas, and from other sports."