The shadow foreign secretary said that she had given the ousted MP until the end of Thursday to withdraw the claim – made in a TV interview on Sunday – but “she refuses to”.
“So that is what we are doing to do, we are having to take legal action,” Ms Thornberry said.
The extraordinary spectacle of one senior Labour figure suing another comes after Ms Flint stepped up her criticism that a pro-Remain faction was to blame for Labour’s election disaster.
The former MP for Don Valley targeted Ms Thornberry, a north London MP, claiming: “She said to one of my colleagues, ‘I’m glad my constituents aren’t as stupid as yours.’”
However, Ms Thornberry ridiculed the source of Ms Flint’s claim, telling the BBC: “Caroline Flint was told by somebody else that I had spoken to somebody else – that person unknown and when unknown and where unknown and she still won’t tell us.”
She insisted: “I would never even think that, let alone say it – it’s a complete lie.”
On Sky News, she said: “People can slag me off, as long as it’s true, I can take it on the chin. But they can’t make up s*** about me – and if they do, I have to take it to the courts.”
Ms Flint said that Putney and Canterbury – two Labour seats in the south – were not a fair exchange for the dozens of northern seats that had been lost to Boris Johnson.
The party had “gone too much towards the metropolitan cities and university towns and away from these core areas and it breaks my heart”, she said.
“I don’t believe anybody who has been the architects of our European policy in the last few years is credible to be leader. I don’t think they can win back these seats.”
The clash came as the starting gun was fired in the race to succeed Jeremy Corbyn, with Ms Thornberry and Sir Keir expected to be among the contenders.
Labour is engulfed in a row about whether Mr Corbyn’s unpopularity or the party's support for a fresh Brexit referendum was mainly to blame for its election disaster.
There is also anger that Mr Corbyn intends to carry on as leader, facing Boris Johnson in the Commons for more than three months, before his successor takes over by the end of March.