Despite "glaring similarities", the lawsuit claims Del Toro, producer Daniel Kraus and studio Fox Searchlight "never bothered to seek or obtain a customary licence" for the rights to the play - or credit Zindel. The alleged similarities are "too egregious to ignore", according to the lawsuit.
David Zindel says his father, Paul Zindel, wrote a 1969 play called, "Let Me Hear You Whisper". the story of a lonely female janitor who works graveyard shifts at a lab that performs animal experiments for military use.
"Shape of Water" story lifted from esteemed playwright?
However, in Let Me Hear You Whisper, the creature is a dolphin rather than a half-man, half-river creature.
"The Shape of Water", co-written by Del Toro and Vanessa Taylor, tells a love story between a mute woman who works as a cleaning lady in a hidden, high-security government laboratory in 1962 Baltimore and a misunderstood aquatic monster.
In a statement, Fox Searchlight denied that the film was based on Zindel's play, calling the infringement allegations "baseless, wholly without merit" and saying the studio "will be filing a motion to dismiss". Richard Jenkins, Octavia Spencer, and Michael Shannon all co-star in the picture.
Kraus, who did not respond to a request for comment, said in a recent interview that he came up with the idea when he was 15 years old, which was around the time of a 1990 television production of Zindel's play, the suit noted.
The studio said it would "vigorously defend ourselves and, by extension, this groundbreaking and original film".
This image released by Fox Searchlight Pictures shows Sally Hawkins, left, and Doug Jones in a scene from the film The Shape of Water.
In a lawsuit filed yesterday, Zindel lists 61 perceived similarities between the film and the play, which has been twice produced for USA television, in 1969 and 1990.
The Shape of Water has already won a best picture Golden Globe and numerous acting and craft awards from film critics' groups in the United States and elsewhere.