Answer: Probably not. Like other sovereign governmental entities, tribes enjoy common law sovereign immunity and cannot be sued. An Indian tribe is subject to suit only where Congress has "unequivocally" authorized the suit or the tribe has "clearly" waived its immunity. There is a strong presumption against waiver of tribal sovereign immunity.
The doctrine of sovereign immunity shields tribes from suit for monetary damages and requests for declaratory or injunctive relief. However, tribal government officials who act beyond the scope of their authority are not immune from claims for damages.
Tribes are also immune from the enforcement of a subpoena, e.g., to compel production of documents. Further, a court cannot compel the Department of the Interior (DOI) or the Bureau of Indian Affairs (BIA)-- fiduciaries for the benefit of tribes--to comply with the Freedom of Information Act (FOIA) and release documents passed between tribes and the agencies unless the communications involve "tribal interests subject to state and federal proceedings." Arguably, if a tribe is immune from state or federal suit, documents exchanged between tribes and DOI or BIA regarding "tribal interests" or "matters internal to the tribe," are exempt from disclosure under FOIA.
Tribal immunity generally extends to agencies of the tribe such as tribal casinos and other business enterprises. As many Idaho citizens flock to tribal casinos, slips-and-falls and other tort claims arising on tribal reservations have increased. Nevertheless, courts routinely dismiss personal injury suits against tribes for lack of jurisdiction.
Therefore, in considering whether to sue a tribe on behalf of an injured party, you must closely evaluate issues of sovereign immunity and waiver. Unless you can show clear evidence of tribal waiver or unequivocal Congressional abrogation, do not waste your time, your client's money, or a court's resources by filing suit. A judge will simply dismiss the plaintiff's claims for damages for lack of subject matter jurisdiction.