In his resignation letter, the 76-year-old representative of Birkenhead called Corbyn "a force for antisemitism in British politics".
West Bromwich East MP Tom Watson, the deputy Labour leader, said: "This is a serious loss to the party and I deeply regret Frank's decision".
He also attacked the "culture of nastiness" in Labour under Jeremy Corbyn's leadership.
Field came under fire after defying the party's leadership and voting with the government on key Brexit legislation.
Mr Field, who has represented the Merseyside seat since 1979 and has faced previous efforts to de-select him, denied he had "jumped before he was pushed" and said he meant to fight the next general election as an independent Labour candidate.
"I will make my own decision about how I deal with this in my own time". "I will be in Birkenhead, people will be talking to me, coming up to me in the street to see whether they want me to have a by-election or not".
The politician, who has represented Birkenhead for almost 40 years, was told by Nick Brown that he would be removed from the party unless he reversed his decision to resign the whip - effectively the rules and policy an MP is bound by.
Frank Field quit with a letter to the party's chief whip accusing the leadership of the left-of-center party of overseeing an "erosion of our core values".
He accused some members of the Birkenhead Constituency Labour Party of "thuggish conduct", and said it was governed by "a culture of intolerance, nastiness and intimidation".
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He repeated that he would remain a member of Labour but added: "I can not, through continuing to take the Labour whip, lend any legitimacy to the most appalling culture which is now dominating national and local Labour Party institutions".
It was Sacks's first comments since the anti-Semitism problem surrounding the political party reached new heights over the past few weeks, causing louder calls for Corbyn's resignation.
He was also applauded by some Conservative MPs, with Home Secretary Sajid Javid tweeting that he was "a man of integrity and principle".
"Anyone suggesting Frank Field has taken the decision on a whim doesn't know their backside from their elbow", Labour MP Neil Coyle has told Today.
He told the Daily Telegraph: "I understand that his constituency party membership has been giving him an incredibly hard time, which is unforgivable and reminds me vividly of the Eighties, when I was involved as a member of the national executive committee in dealing with these people, particularly from Merseyside".
"It's so sad to see someone like Frank Field trashing Labour's anti-racist record".
He wrote: "I am resigning the whip for two principal reasons".
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A 2016 inquiry, carried out by Shami Chakrabarti, concluded that while the Labour Party was not overrun by anti-Semitism, there was an "occasionally toxic atmosphere". Some in the party allege that Corbyn, a longtime critic of Israel's policies toward the Palestinians, has allowed anti-Semitic abuse to go unchecked.