Executives at Bagdasarian Productions, along with writer Janice Karman, allege "substantial copyrighted" portions of a screenplay Karman wrote were used in last year's Alvin and the Chipmunks: The Squeakquel without permission.
The lawsuit claims Karman, who is married to the son of late Chipmunks creator Ross Bagdasarian, Sr., penned a screenplay for the film and was offered a compensation fee from the studio, which she turned down as insufficient.
The family's complaint reads: "Karman's provision of her screenplay writings to Fox was conditioned upon the payment of adequate compensation for those writings and her attendant services, which Karman never received."
But Fox studio executives are planning to battle the suit, calling it "completely without merit".
A statement from Fox adds, "We look forward to resolving our differences and, in the meantime, we are continuing to move forward with this franchise."
The plaintiffs want Karman to be made a co-owner of the script, and argue she should receive half of all profits "attributable to The Squeakquel's screenplay". The animated movie raked in more than $442 million (£295 million) at the worldwide box office, reports Reuters.