BBC director of television Danny Cohen has pledged that the corporation is "not going to have any more panel shows with no women on them", branding the exclusion "not acceptable."
But Toksvig, 55, the long-time host of satirical Radio 4 show The News Quiz, suggested that recruiting more female hosts would be a more desirable way of correcting the imbalance because more women would want to join their panels.
In the TV Times interview, she also criticised the dearth of older women on TV, saying that "wonderful" older female faces "wouldn't be difficult to find".
Asked why so many quiz shows are presented by men, Toksvig, who is the new Fifteen To One host, replied: "I don't know why that is, and it's slightly ridiculous.
"I know there has been a great push to get more female panellists on television, and I don't think that's the answer.
"But if you get more female hosts, you'll immediately have more women taking part, without it causing any trouble at all. They bring a different tone and make it easier for other women to feel comfortable about participating, so I would be a big fan of more female hosts on quiz shows."
Toksvig, who recently renewed her wedding vows with her partner at a public ceremony to celebrate the introduction of gay marriage in the UK, said that older women were still disappearing from TV screens.
"I'm not just one of the few female hosts on television today, I'm also a woman of a certain age," she told TV Times.
"I'm 55, at a point where females tend to disappear from our screens. There are lots of great women. I just don't know why our sell-by date seems to arrive sooner than for boys."
Her comments come after Mock The Week host Dara O'Briain said that he opposed the way that the BBC had publicly aired its decision to get more women on panel shows.
"I have nothing against this idea that there be women on panel shows or indeed that quietly you ask panel shows to make sure there are women on panel shows. My only objection was to announcing it," he said.
Comic Victoria Wood has criticised the laddish culture of "testosterone-fuelled" comedy panel shows like Never Mind The Buzzcocks, while Jo Brand said she no longer considered appearing on Mock The Week.