An article from Mexican Total blog, discusses the ways how foreigners could secure their money on Mexico and Mexican Banks.
Non-Mexican has 3 options of banking accounts that they could open. These are the Mexican Peso cheking account, US Dollar checking account, and the certificate deposit. Both of the checking account require a minimum of $500 - $1,000 initial deposit and usually have a small interest rates. The certificate deposit is more like of a time deposit where you would be restricted to withdraw your money for a specific period of time.
More about banking offers for foreigners, on the link below.
Link: news Banking Basics in Mexico