Writing on Twitter, Lynch said he had not been given enough money "to do the script in the way I felt it needed to be done".
"This weekend I started to call actors to let them know I would not be directing," he added.
Lynch's departure casts doubt on the revival, which was commissioned by US network Showtime last October.
The auteur, whose credits include Blue Velvet and Mulholland Drive, created the cult drama with Mark Frost in the 1990s.
Revolving around the murder of teenage schoolgirl Laura Palmer, the show was a precursor of dense, cinematic TV shows like The Sopranos and The Wire.
It won three Golden Globe awards in 1991, including best TV series and best actor for Kyle MacLachlan.
MacLachlan played Special Agent Dale Cooper, an FBI agent who got drawn into the seedy town of Twin Peaks as his murder investigation took several surreal turns.
He was due to reprise the role in the Showtime revival when production began later this year.
Lynch and Frost have already written scripts for the nine episode series, which was due to air in 2016, marking the 25th anniversary of the original finale.
In his statement, Lynch said: "I love the world of Twin Peaks and wish things could have worked out differently."
However, he hinted the show might go ahead in his absence.
"Twin Peaks may still be very much alive at Showtime," he wrote.
Soon after his comments were published on Twitter, Showtime released the following statement.
"We were saddened to read David Lynch's statement today since we believed we were working towards solutions with David and his reps on the few remaining deal points.
"Showtime also loves the world of Twin Peaks and we continue to hold out hope that we can bring it back in all its glory with both of its extraordinary creators, David Lynch and Mark Frost, at its helm."
Director David Lynch has confirmed he will not direct the sequel to Twin Peaks, citing disagreement over money.