The company - which is based in Menlo Park, California - have been granted authorisation to cart samples such as blood tests from labs to hospitals and back using their automated drones.
It is due to take to the skies next month, with more units set to be installed in the next year or so.
Andreas Raptopoulos, co-founder and CEO of Matternet, told The Verge: "These types of diagnostics that need to be transported are urgent in nature and they are on demand. They have to wait for a courier, sometimes they get taxis to do this type of thing - and when you have a system like this, that is autonomous and reliable, it completely transforms operations."
To coincide with the new service, the company have unveiled their Matternet Station - a special type of "postbox" of around two square metres that will be installed on rooftops, for example, and allow the sending and receiving of packages.
In a press release, they added: "The Matternet Station occupies a small footprint of approximately 2 square meters and can be installed at ground or rooftop locations. It is equipped with technology that guides the Matternet M2 Drone to precision landing on the Station's platform.
"After landing, the Station locks the drone in place and automatically swaps its battery and payload. A user is able to send a package to another location by simply scanning it into the Matternet Station, or receive a package from the Station by scanning a QR code. Each Station comes with its own automated aerial deconfliction system that manages drone traffic over the Station."
Matternet are hoping to roll out their service in the Germany and the UK if Switzerland is a success.