Rudd said she no longer believed leaving the EU with a deal was the Boris Johnson government's "main objective", the BBC reported on Saturday.
Rudd described the sacking of 21 Tory MPs on Tuesday as an "assault on decency and democracy".
No. 10 said it was "disappointed" by the resignation of a "talented" minister.
But a spokesperson added that "all ministers who joined the Cabinet signed up to leaving the EU on October 31 come what may".
A senior government source said "resignations to chase headlines won't change the fact that people want Brexit done so that government can deliver on domestic priorities".
Labour said Rudd's resignation showed the government was "falling apart".
The MP for Hastings and Rye, who supported Remain in the 2016 referendum, said her resignation had been "a difficult decision".
"I will be considering my position - whether I will stand as an independent Conservative should there be an election coming up," she told the Sunday Times.
In her resignation letter to PM Boris Johnson she said: "I joined your cabinet in good faith: accepting that 'No Deal' had to be on the table, because it was the means by which we would have the best chance of achieving a new deal to leave on October 31.
"However, I no longer believe leaving with a deal is the government's main objective."
( With inputs from IANS )