Dr. Frederick Frankenstein (Gene Wilder) is a respected lecturer at an American medical school and is more or less happily (though blandly) engaged to the tightly wound Elizabeth (Madeline Kahn). Frederick becomes exasperated when anyone brings up the subject of his grandfather, the famous mad scientist, to the point of insisting that his name is pronounced "Fronk'-en-steen".
A solicitor informs Frederick that he has inherited his family's estate. Traveling to said estate in Transylvania, Frankenstein meets his comely new lab assistant Inga (Teri Garr), along with the household servants Frau Blücher (Cloris Leachman) and Igor (Marty Feldman) (who, after hearing Frederick claim his name is pronounced "Fronkensteen" counter-claims that his is pronounced "Eye'-gor.")
Inga assists Frederick in discovering the secret entrance to his grandfather's laboratory. Upon reading his grandfather's private journals the doctor is inspired to resume his grandfather's experiments in re-animating the dead. He and Igor successfully exhume and spirit away the enormous corpse of a recently executed criminal, but Igor's attempt to steal the brain of a revered scientist from the local "brain depositary" goes awry, and he takes one labeled, "Do Not Use This Brain! Abnormal" instead.
The doctor and reassembled monster (Peter Boyle) are elevated on a platform to the roof of the laboratory during a lightning storm. The experimenters are first disappointed when the electrically charged creature fails to come to life, but the reassembled monster eventually revives. The doctor assists the monster in walking but, frightened by Igor lighting a match, it attacks Frederick and must be sedated.
Meanwhile, the local townspeople are uneasy at the possibility of Frederick continuing his grandfather's work. Most concerned is Inspector Kemp (Kenneth Mars), who visits the doctor and subsequently demands assurance that he will not create another monster. Upon returning to the lab, Frederick discovers that Frau Blücher is setting the creature free. After she reveals the monster's love of music, and her own romantic relationship with Frederick's grandfather, the creature is enraged by sparks from a thrown switch, and escapes from the Frankenstein castle.
While roaming the countryside, the Monster has frustrating encounters with a young girl and a blind hermit (cameo by Gene Hackman); these scenes directly parody ones from the original Frankenstein movies. Frederick recaptures the monster, wins him over with flattery, and finally fully acknowledges his heritage.
After a period of training, he offers a theater full of illustrious guests the sight of "The Creature" following simple commands. The demonstration continues with Frederick and the Monster launching into the musical number "Puttin' on the Ritz", complete with top hats and tails (and no small amount of clumsiness on the monster's part), which ends disastrously when a stage light explodes and frightens the monster. He becomes enraged and charges into the audience where he is captured and chained by police.
After being tormented by a sadistic jailer who smiles, the Monster escapes again, then kidnaps and ravishes the not-unwilling Elizabeth when she arrives unexpectedly for a visit. Elizabeth falls in love with the creature due to his inhuman stamina and his enormous penis.
The townspeople, led by Inspector Kemp, hunt for the Monster. Desperate to get the creature back and correct his mistakes, Frederick plays music and lures the Monster back to the castle. Just as the Kemp-led mob storms the laboratory, Dr. Frankenstein transfers some of his stabilizing intellect to the creature who, as a result, is able to reason with and placate the mob.
The film ends happily, with Elizabeth married to the now erudite and sophisticated Monster, while Inga joyfully learns what her new husband Frederick got in return from the Monster during the transfer procedure (the Monster's gigantic penis).