Emerging autonomous (driverless) delivery services are increasing access to unhealthy foods and beverages. Home delivery services using autonomous vans, street bots, and drones are already operating in multiple countries (e.g., China and the US), and drone delivery trials are currently underway in Australia. As these services proliferate, understanding public support for regulation will be critical due to community acceptability being a key driver of governments’ willingness to implement restrictive policies. This study aimed to examine public support for seven autonomous delivery service policies designed to minimise the potential public health impacts of increased unhealthy food availability via these services. A sample of 3,000 Australian adults completed an online survey assessing lifestyle behaviours and policy support. Support was moderate across the assessed policies, with a mean score of 3.58 on 5-point scales. Support was strongest for regulating drone deliveries, with three-quarters endorsing banning late-night deliveries and limiting the number of delivery drones operating above a suburb at the same time. The two policies receiving only minority support related to applying taxes and restrictions on delivery frequency (both 40%). While support was significantly higher for most policies among females, older adults, and those with self-reported healthier diets and less frequent fast-food consumption, the magnitude of these differences was typically small. Overall, these findings are encouraging because drone delivery is the primary autonomous delivery technology emerging in Australia, and it was the area where support was strongest. In addition, regulating the operational characteristics of autonomous delivery services is likely to be more practically feasible rather than attempting to influence consumer behaviour once the services are widely available. Policies to restrict drone deliveries may therefore provide a practical starting point. Overall, these findings suggest that anticipatory and publicly supported regulation may provide a viable pathway to mitigate health harms from ubiquitous autonomous delivery services.