The 19 cases, connected to a small number of households in the Acklam, Linthorpe and town centre end of Marton Road area, have all been confirmed this week.
All those who have tested positive are self-isolating in line with national guidance.
Middlesbrough Council environmental health officers are carrying out contact tracing to control the spread of infection.
Anyone known to have been in close contact with someone who has tested positive is being advised to get a test and self-isolate for 14 days.
The town’s infection rate remains relatively low compared to areas where local restrictions are in place, but the public are being urged to be extra vigilant.
Middlesbrough Mayor Andy Preston said: “We’re taking strong action and alerting the public to protect people’s health and jobs.
“I promise to keep everyone informed of developments as the situation progresses. Rest assured, we will do what’s best for Middlesbrough.”
South Tees Joint Director of Public Health Mark Adams said: “Although we have quickly established these cases are connected, they act as a reminder to everyone in Middlesbrough to take Covid-19 seriously.
“We have prepared for situations like this one and are reacting fast.
“I urge everyone in Middlesbrough to do all they can to protect themselves and others.
“Cover your face in public places, wash your hands regularly and keep your distance from others. Anyone with symptoms should self-isolate and book a test online or by calling 119.”
Anyone with a high temperature, a new continuous cough or a loss or change to their sense of smell or taste should isolate and book a test.
A testing centre at the unused Sainsbury’s site close to the Riverside Stadium is open from 8am until 8pm seven days a week and can test 800 people per day.
Middlesbrough Council is working with Public Health England’s regional Health Protection Team to manage the situation.