The demand follows a finding by government-appointed committees that the firm was operating illegally and had understated its gold exports.
Acacia's website says that it has declared all materials produced and has paid royalties and taxes in full.
The UK-listed firm's shares were down 7.7% in morning trade in London.
Earlier this month, Tanzania passed two new mining laws that contain sweeping changes to the legal and regulatory framework of the mining industry.
An export ban on gold and copper concentrate exports has been in force since March.
Acacia, which is majority-owned by Canadian firm Barrick Gold, has said the continuation of the ban will hurt its ability to conduct future business in Tanzania, since it covers 50% of its production.
"The security of the 36,200 indirect and induced jobs that rely on Acacia's mining operations, as well as the company's ability to invest in education, infrastructure and health projects will all be under threat."