The Medicaid Office in New Mexico can assist with questions about the New Mexico Medicaid Program. This program is state funded for individuals and families in need to help pay for medical care. This could include coverage for doctor visits, hospital visits, dental care, vision care and other medical needs. Below we list the New Mexico Medicaid office phone number, address and online website so you can contact them to see if you are eligible for the New Mexico medicaid program. The department that handles the Medicaid Program in New Mexico is called Department of Human Services of New Mexico.