Speaking in parliament yesterday Maneesh Gobin said the current insurance claims, both from government as well as individuals and companies around the republic totalled Rs1.51bn ($37.8m).
However, numbers are still being compiled and are expected to be considerably higher.
The Panama-flagged newcastlemax veered from its course, grounding on coral reefs off the southern coast of Mauritius in July.
The ship leaked bunker fuel and split in two, creating one of the worst ecological disasters Mauritius has experienced.
In the wake of the disaster, the government set up an online resource for locals to lodge their damage claims.
The stern of the ship remains lodged on the same reef, while the front three-quarters of the ship was towed out to sea and scuttled in August.
The vessel was insured by Japan P&I Club.