Check out this video shot during an Uber ride last week in Nashville ... you see the driver waving around a huge breathalyzer in his right hand as he drives down a street.

The passenger, Kyle, tells TMZ ... he noticed a sudden beeping noise in the car. He says the driver told him it was a safety feature in his vehicle causing the noise, and then reached under his seat to pull out the breathalyzer. Kyle says the driver blew into it, and the trip continued.

In the video, you hear the driver say, "I just had this put in today, I haven't perfected it."

The rider reported the troubling incident to Uber and requested a refund, and it hit him back with a generic response and a measly $5 credit to his account.

Doesn't seem like a great response to finding out your driver possibly has a DUI that requires him/her to intermittently blow into a device, just to keep the engine running -- however, an Uber rep says the driver was using a family member's car because his car was getting repairs. Uber says the device belonged to the driver's relative.

We're told the driver is not being disciplined because he had registered the relative's car as a secondary vehicle on his account.

The ridesharing app has a policy that people cannot drive for Uber if they've been convicted of DUI within the past 7 years, and the company claims it conducts criminal background checks and driving record checks to ensure its drivers meet certain safety standards.