According to the lawsuit – filed in a federal court – Federal Insurance Company has refused to pay out for the disruption.
Documents lodged in the court accuse the insurers of breach of contract, and breach of the implied covenant of good faith and fair dealing.
Paramount’s team say the studio was covered for losses exceeding $100m (£73m), but Federal Insurance Company argued, the suit says, that some of the losses claimed were only covered to a value of $1m (£730,000).
Paramount is claiming the insurer only paid a “small portion” of the losses, “denying coverage for the majority of them”, and therefore “breached the parties’ contract”.
The 22-page court filing said: “Federal’s conduct is contemptible and has been done with a conscious disregard of Paramount’s rights, constituting oppression, fraud, and/or malice.”
Paramount is seeking unspecified damages as part of the suit.
Other film and television productions have sued their insurers for failing to pay out due to pandemic problems.
Ben Affleck’s film Hypnotic and Apple TV+ drama The Morning Show have also launched lawsuits.