Following the party's annual conference last weekend, the Lib Dems committed to revoke Article 50 if they make it into power and stop the Brexit process in its tracks.
Speaking to The House Magazine, shadow foreign secretary Ms Thornberry said: "The Lib Dems have gotten kind of Taliban, haven't they? They've said they're just going to revoke, there's not going to be another referendum.”
Ms Swinson tweeted her displeasure at being compared to the fundamentalist group.
She said: "Comparing a UK political party to the Taliban is ludicrous. Emily is the shadow foreign secretary, and should use language that reflects the importance of that role."
Chuka Umunna, who joined the Liberal Democrats after Leaving Labour and Change UK, also condemned Ms Thornberry for her comments.
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Mr Umunna said: “Emily Thornberry should withdraw her inappropriate remarks.
“Language counts - comparing the Lib Dems to a murderous organisation is no laughing matter.
“It is also grossly insulting to over 23,000 of her constituents who signed the parliamentary petition for Article 50 to be revoked.”