On January 1, 2019, a new law went into effect requiring all cars traveling on federal roads to have civil liability insurance. Civil liability insurance is third party liability insurance and covers damages to third parties and property. This is much like the temporary auto insurance you must have as a foreigner traveling into Mexico.
While the law was approved back in April of 2013, it was not put into enforcement on all vehicles until this year, and violators face fines ranging from 2,000-4,100 pesos. When this law was first passed, it only applied to newer cars and certain values but as time went on, it applied to older models and now all cars.
The obvious goal here is to help protect victims of traffic accidents, which on average leave 44 dead and 369 injured every day. Vehicle accidents are the second cause of death in Mexico.
The law sets minimum limits for civil liability insurance for persons and for property damage; check the current limits when you buy. Federal police have already started random checks on federal roads to ensure people carry the required insurance.
The law is Article 63 Bis of the Ley de Caminos, Puentes y Autotransporte Federal. A U.S. or Canadian policy does not meet it: Baja Bound notes that US and Canadian insurance is not considered proof of financial responsibility under Mexican law. For the documents and permits you need before you drive down, see what you need before you drive into Mexico.
Want it done before you leave? Compare Mexican car insurance.