The longtime leader and AfD spokesperson said he could no longer fend off the party's more extremist faction. He had already announced his intention to step down as co-chair, but now plans to leave the party entirely.
However, a party summit in December to elect a successor was canceled due to the COVID-19 pandemic.
Aims to stay on as MEP
Meuthen, who was elected co-leader of the party in 2015, said he wants to keep his job in the European Parliament.
He said he is already in talks with other parties, but would not confirm which ones.
Meuthen has long been at odds with much of the rest of the AfD and had, over the past two years, repeatedly argued for his party to take a more moderate course.
In doing so, he made enemies, especially in the far-right movement around the central state of Thuringia's leader Björn Höcke.
Far-right AfD still holds appeal in the east
Meuthen's relationship with the party’s recently elected parliamentary leaders, Alice Weidel and Tino Chrupalla — who also shares the party chair position with Meuthen — has also been tense.
Both Weidel and Chrupalla have continued to support the hardliners within the party.
Meuthen decries AfD's 'cult-like' COVID stance
In his interview with public broadcaster ARD, Meuthen also complained that the AfD had become something of a cult in its politics around the COVID-19 pandemic.
Germany has seen widespread protests in opposition to the government handling of the health emergency over the past 18 months, which intelligence agencies have said were driven by the far-right.
At best, Meuthen said he can only see a future for the AfD as a regional party for eastern Germany.
The AfD's federal executive board issued a muted response to the resignation.
A party statement said it had "noted" the decision and thanked Meuthen for "the further development of the AfD as the only opposition party in Germany."
AfD co-leader hits out at Meuthen
However, party co-leader Weidel was sharply critical of the decision.
In an interview with the Stuttgarter Nachrichten and Stuttgarter Zeitung newspapers, she accused Meuthen of "throwing mud at the party he has long presided over," which she said "does not speak to the quality of his character."
Weidel said Meuthen's resignation may have been linked to plans to lift his immunity as an MEP over a scandal involving illegal party donations.
On Thursday, the EU Parliament's Legal Affairs Committee had voted to strip Meuthen of his immunity, which bolsters the chances that Berlin's public prosecutor's office will open an investigation against him over the affair.
Last year, the AfD was ordered to pay €500,000 ($558,000) in fines after being found to have accepted donations from a German-Swiss property billionaire three years earlier.
Meuthen said his decision to leave was not related to the lifting of immunity. He had earlier said a potential probe would be a chance to clear his name.