The Council is urging everyone who shares transport to wear face coverings to stop the spread of Covid-19 and allow people to venture out with confidence.
The call comes after recent contact tracing work found a small number of positive tests linked to individuals who share cars to and from work.
There is also concern over a minority of people using taxis who are not covering their faces.
Middlesbrough Mayor Andy Preston said: "Our local taxi drivers provide a great service throughout the town and their safety, as well as their passengers' safety, must be protected.
"I want people to be able to get out and about with confidence. Businesses around Middlesbrough need our support and the more people that cover their faces the less likely it is the virus can spread.
"Wearing a face covering is a small price to pay so we can enjoy more of the freedoms that have returned in recent months."
In addition, taxi drivers are being reminded of the importance of keeping a record of their passengers to support NHS Test and Trace.
Private Hire Operators keep customer records through booking systems, but details are not routinely collected by Hackney Carriage drivers.
Mahrouf Hussain, Chairman of the Middlesbrough Hackney Carriage Association, said: "Our members would like to see passengers wearing face coverings for all journeys to protect drivers' health and wellbeing and of course passengers' own safety."
A spokesperson for Boro Cars said: "While it isn't a legal requirement for drivers to wear face coverings, we issue them and PPE to all of our drivers free of charge.
"Many of our drivers and customers are already wearing face coverings and we urge everyone to work together and do the same to help stop the spread of the virus and keep Middlesbrough safe."
Drivers of both Hackney Carriages and private hire vehicles are entitled to refuse journeys if a passenger refuses to wear a face covering without reasonable justification.
Guidance issued by the Department for Transport advises people not to share a vehicle with those outside their household or support bubble, where possible.
Where this is not possible, the guidance advises:
- Sharing transport with the same people each time
- Opening the windows for ventilation
- Wearing a face covering for the duration of the journey
- Considering seating arrangements to maximise distance between people in the vehicle - e.g. leave seats some free.
- Cleaning the vehicle between journeys, including door handles and other areas that people may touch.
The Council is continuing to monitor new coronavirus cases closely and is advising anyone with mild symptoms to book a free test online or by calling 119.
- For the latest local updates and information, visit middlesbrough.gov.uk/covid19
For information on local help and support, visit Help Boro at www.middlesbrough.gov.uk/helpboro or call Middlesbrough Council's support line 01642 729777
The latest advice from Government and Public Health England can be found at https://www.gov.uk/coronavirus