Yes, some of the most popular ductless systems are compatible with the Nest Thermostats. However you will often need to purchase both the Nest Thermostat and a compatible adapter.
The following setup will work for Mitsubishi ductless systems with the Nest Thermostat:
How does Nest Work With Ductless Systems?
You will need to make sure the power is off, install the attached thermostat adapter interface and then wire the new Nest thermostat into the thermostat adapter interface.
Once you have connected the Nest to the thermostat interface you can then turn back on the power to the ductless system and start setting up your Nest Thermostat.