Smart meters measure electricity usage and communicate this information to the supplier using short bursts of radio waves or low level radiofrequency (RE) electromagnetic energy (EME).
There is no established scientific evidence that this low level exposure to RF EME causes any health effects.
Smart meters emit lower levels of RF EME than many common household devices like mobile phones, microwaves, and baby monitors. (source)
For more information on smart meter safety, we recommend reading this guide on Smart meters and health from the Australian Radiation Protection and Nuclear Safety Agency.