The driver's station wagon hit the 20-year-old rider on the Princes Highway in Narre Warren on Thursday.
The motorist was not injured and stopped to help the rider, who died at the scene.
"The driver of the car was spoken to and has been cleared of any wrongdoing," police said in a statement.
They have urged anyone who may have seen the crash or have dashcam footage to contact Crime Stoppers.
Health Minister Martin Foley said he was concerned by the incident.
"As we've seen last night, this can be fatal, as we have seen in my own community people riding on the footpath is dangerous," he told reporters on Friday.
Melbourne is trialling an e-scooters rental scheme in the City of Melbourne, Port Phillip and Yarra, which allows people to ride hired scooters in bike lanes, on low-speed roads and shared paths.
Mr Foley said Narre Warren was not part of the scheme.
"There are safety rules in place for this trial, please follow them," he said.
VicRoads says many people have been riding e-scooters illegally on roads and footpaths, putting safety at risk.
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