At-Risk Youth Medicaid Protection Act of 2017 This bill amends title XIX (Medicaid) of the Social Security Act to specify that a state Medicaid program may not terminate a juvenile's medical assistance enrollment because the juvenile is incarcerated. A state may suspend enrollment while the juvenile is an inmate, but must restore enrollment upon release without requiring a new application or any other action unless the individual no longer meets the eligibility requirements for medical assistance. A state must process an application submitted by, or on behalf of, an incarcerated juvenile, notwithstanding that the juvenile is an inmate. A "juvenile" is an individual who: (1) is under 21 years of age; or (2) has aged out of the state's foster care system, was enrolled in the state plan while in foster care, and is under 26 years of age.