@Tom is correct, and to expand on Johns-305 recommendation, here is Carnival's web link:
TRAVEL DOCUMENTATION U.S. PERMANENT RESIDENTS
Carnival requires guests to provide proper travel documentation in order to travel. The documentation is required at embarkation and throughout the cruise and is the responsibility of the guest. Our policy states that any guest traveling without proper documentation will be denied boarding the ship and will be under full penalty, and therefore, will not be offered a refund or a replacement cruise. Guests must contact the appropriate embassy or consulate of the countries they will be visiting for specific travel documentation requirements. Carnival assumes no responsibility for advising guests of Immigration requirements.
On occasion, U.S. Permanent Residents may be asked to surrender their Permanent Resident Card and/or passport at time of check-in. This document will be returned upon completion of the immigration inspection at the time of debarkation.
- Guests are required to carry a valid Permanent Resident Card (also known as ARC or Green Card), that includes a photo I.D. In addition, U.S Permanent Residents must contact the appropriate embassy or consulate of the countries they will be visiting for specific travel documentation requirements. Carnival assumes no responsibility for advising guests of Immigration requirements.
- Please Note: If a Permanent Resident Card does not have an expiration date on the front, then it is a very old version and it is recommended that the guest applies to renew it. Filing instructions and forms are available at www.uscis.gov.
- Photo I.D. Information: If the Permanent Resident Card does not include a photo I.D., a non-expired government-issued photo I.D. is required of all guests 16 years of age or older such as a Driver’s License, Driver’s Permit or government-issued identification card (city/state/federal).
Consulate General of México notice advising that, among others, those with US permanent residency and a valid passport do not require a visa to enter the country:
A. Effective March 1st 2010, all visitors traveling to Mexico either by air, land or sea are required to present a valid (non-expired) Passport or Travel Document from their country to enter Mexico.
B. With the purpose of facilitating and promoting travel to Mexico, effective May 2016 all those foreign nationals, regardless of their nationality, visiting Mexico for tourism, business or transit are NOT required to obtain a Mexican visa IF they hold a valid (non-expired) Visa or Permanent Residence of any of this countries: United States of America, Canada, Japan, United Kingdom or Schengen area (European Union).