Director Guillermo del Toro and the Fox Searchlight studio are being sued by the family of late Pulitzer-winning playwright Paul Zindel.
They denied the allegations about the film, which is up for 13 Oscars.
The otherworldly film stars Sally Hawkins as a mute cleaner who falls in love with an amphibious man.
It has already won Golden Globes and its Oscar nominations include best director for del Toro and the prestigious best picture, leading the pack with 13 nominations.
Hawkins is also up for best actress for her portrayal of Elisa Esposito.
Votes are currently being cast for the awards, which take place in Los Angeles on 4 March.
Image copyrightTWENTIETH CENTURY FOXImage captionGuillermo del Toro, pictured on set, said he had not read or seen the play before making his film
Del Toro has said he had never heard of the play before making The Shape of Water, and neither had any of his collaborators.
Zindel's family sued the studio, director and others on Wednesday in a California court, saying the film is "in many ways identical" to his play, Let Me Hear You Whisper.
The play tells the story of Helen, a "little old cleaning lady" newly hired to work in a laboratory where experiments are being carried out on dolphins.
She develops a rapport with one of them and plays it music as it makes attempts to speak.
Fox Searchlight said it would "vigorously" defend the "ground-breaking and original film".
"These claims from Mr Zindel's estate are baseless, wholly without merit and we will be filing a motion to dismiss," a spokeswoman said.
"Furthermore, the estate's complaint seems timed to coincide with the Academy Award voting cycle in order to pressure our studio to quickly settle."
Lawyer Marc Toberoff claimed in court there are at least 61 similarities between the two works, saying both are 1960s Cold War stories about an unmarried janitor and her relationship with an aquatic creature.
In the case of the play, it is a dolphin, while in the film it's a humanoid creature with fins and gills.
He said: "The Shape Of Water, though presented to the public as a highly original work of fantasy/science fiction, in reality, brazenly copies the story, elements, characters, and themes from a work by Pulitzer Prize-winning author Paul Zindel."
The case refers to an interview in which del Toro said author Daniel Kraus told him, in 2011, of an idea "about a janitor that kidnaps an amphibian-man from a secret government facility".
Kraus, also a defendant in the case, is said to have come up with the idea as a teenager.
Toberoff said that would have been in 1990 - the year a television adaptation of Zindel's play aired.
'We had to act'
His son David Zindel said: "We are very grateful for the spontaneous outpouring on social media that first brought this injustice to our attention.
"This troubling matter was raised with Fox five weeks ago but was met with inertia.
"The glaring similarities between the film and our father's play are too extensive for us to ignore and so we had to act."
The family is seeking damages and costs.
It's not the first time the film has been accused of plagiarism - earlier this year, the Netherlands Film Academy ruled The Shape of Water did not have any links to a short film called The Space Between Us, after some viewers claimed there were similarities.
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