Uber says claims a Melbourne driver fell asleep at the wheel are "very concerning" and the ride share company is investigating.

A young woman, named Angelica, filed a complaint with Uber after her driver allegedly fell asleep and drifted across lanes on the Eastern Freeway early on Sunday.

"He actually dozed off and went left four lanes, and actually went off an exit, until he woke up," she told Radio 3AW on Tuesday.

Angelica, who did not give her surname, says her trip from the CBD to Wantirna South also took twice as long as usual, because the sleepy driver kept changing course.

Uber responded on Tuesday afternoon, saying they were investigating the matter.

"What has been described is very concerning," a spokesperson told AAP.

"We take reports of unsafe driving very seriously."

Angelica filed a complaint with Uber and received a refund, but she said the driver "should not be on the roads".

Uber said dangerous driving breached guidelines and can result in the driver losing access to the app.

The company said it continued to work on safety improvements and urged riders with safety concerns to make contact through the app.