Ms Swinson, the MP for East Dunbartonshire, took the Today Programme host to task over a secret recording made of Mr Humphrey’s joking about his colleague Carrie Gracie’s campaign for equal pay.
He was recorded speaking to BBC North America editor Jon Sopel, making light of the suggestion that other senior correspondents were “earning too much” and adding: “She’s actually suggested that you should lose money; you know that, don’t you?”
Ms Gracie resigned from her post as BBC China Editor after failing to secure equal pay with male colleagues, and recently told a committee of MPs that the corporation treated female staff demanding equality as “some kind of enemy”.
Interrupting his guest, the presenter replied: "I wrote an email to Carrie Gracie immediately after that exchange, as a matter of fact I did. And she replied.
"Quite what this has to do with what we’re discussing here I fail to see but there we are. That has answered your question."
Ms Swinson said she was “very glad to hear that” and joked: “It wouldn't be the first time a question has been thrown in at the end.”
A wounded Mr Humphreys said: “It wouldn’t but usually they are slightly more relevant, because this is entirely irrelevant, but however, there we are, I’ve answered your question.”
It was recently revealed that the Today presenter was among several high-profile male figures at the BBC who have taken pay cuts in a bid to close the pay gap at the corporation.
Mr Humphreys took home between £600,000 and £649,999 in 2016/17.
Earlier in the interview, he asked Ms Swinson, who was on the cross-party committee that drew up new measures to combat harassment in parliament: “So what is sexual harassment?”
Mr Humphreys said: “Let’s go back to the old cliche of if a young man asks a young woman out for a drink that evening, that isn’t sexual harassment, is it?”
She replied that “it’s really not all that complicated” and said: “If you’re inviting someone for a drink in a particularly sexual way then I think you maybe need to check your chat up lines.
“There's obviously plenty of ways in which you can respectfully ask somebody out without putting your hand on their bum without being crude and lewd or referencing them in a sexual way, and I just think that the argument that it’s possible for anyone to ask someone out is just a nonsense and a distraction.”
Mr Humphreys later suggested it was “slightly bizarre” that MPs will be asked to undergo training in sexual harassment, prompting Ms Swinson to respond: “The assumption that everybody knows what sexual harassment is is not one that we should take for granted.
“You asked me what the definition was at the start of the interview.”
The presented said he was “looking for a specific definition”, adding: “But I’d like to think that I know, most of us would, wouldn’t we?”
The Lib Dem MP replied: “I would like to think that you did too, but I don't think we should all make those kinds of assumptions.
“Training is an important part of the cultural change that we need.”