Funny Females - founded by Okse, Jane Hill, Ashley Frieze, Bethany Black and Rob Coleman - will run at various venues nationwide from June.
The new competition has the stated goal of celebrating female stand-up comedy. Competitors will be offered a small share of proceeds on a door-split basis, rather than be charged to enter the competition.
Okse said: "I was absolutely outraged that Funny Women are charging this year. It gives the message to new acts that this sort of thing is acceptable, and it's not."
Hill added: "Many of the female comedians I know have negative stories about their experience with the Funny Women competition.
"A competition like that should encourage comedians, not undermine them. Plus, to promote themselves as a 'friendly and supportive' competition and then charge to enter is just ridiculous."
Frieze said: "We hope that this proactive and constructive approach will show both the Funny Women organisers and their prospective customers how a comedy competition can nurture and encourage new talent."