The test was scheduled for March 16-18 at the Italian circuit, located in the north of Milan.
The coronavirus death toll in Italy has risen to 14 people, with over 500 infections detected.
As a safety precaution, ITR said the test will now take place at the Hockenheim circuit in Germany on March 16-19.
"It's become increasingly apparent that the spread and containment of the coronavirus is sadly affecting society in many different and deepening ways," said ITR managing director Marcel Mohaupt.
"With the safety and well-being of everyone at the forefront of our thinking, we took the decision to relocate our pre-season test to a different venue.
"We are extremely grateful to everyone at Monza and Hockenheim for their co-operation in this matter, and we look forward to visiting Italy in the summer for DTM's first-ever event at this legendary circuit."
The 2020 season is scheduled to race at Monza at the end of June, but ITR said there have been no changes to that plan as of yet.