The move should help more people get to doctors when they need to see them without having to perhaps rely on public transport. Around 23 percent of Arizona residents are enrolled with the state's Medicaid agency, so the rideshare option could benefit more than a million people right out of the gate.

Lyft wrote in a blog post that more states are starting to add ridesharing as a covered transportation option under their Medicaid programs. Florida and Texas also brought laws into force on that issue in recent months.