Welsh-born Ms Collier was an Edinburgh Fringe Festival finalist in the 2013 So You Think You're Funny? awards - the leading competition for amateur stand-ups which has helped launch the careers of Lee Mack and Peter Kay.
She said she was "overwhelmed by the lovely support". Mirth Control said "we apologise unreservedly for any offence caused" and that Ms Collier would be offered gig opportunities at other venues.
The company, founded by comedian Geoff Whiting in 1998, is the largest independent comedy booker in the UK. It said it "prides itself on championing women in comedy".
In a statement published on the company's website it added: "We will not accept a relationship with any client who wishes to exclude women entirely from all bills, this is a consistent policy that has spanned many years. However this request was not to place any 'ban' on female comics only to temper the numbers in order to suit their clientele."
Last month the BBC provoked controversy when it said it would no longer broadcast all-male panel shows following criticism of a lack of female contributors to hit shows including QI, Mock the Week and Have I Got News For You.
Comedian Dara O'Brian, who presents Mock the Week, said it could lead to accusations of tokenism.
Mr Whiting said he had compered a previous event at the venue, a coffee shop in Surrey, in which three women appeared.
"We are glad that this important subject has come up for discussion and our policy of supporting and promoting female comedians is central to our core philosophy and will only be strengthened by an event such as this, indeed it has increased our resolve to ensure that they are given even more opportunities in future to perform for us and develop their craft at all the clubs with which we are associated," the company added.
No one from the venue responded when asked to comment.
- Independent
