The Indian High School in Oud Metha has assured parents and said sanitisation work has been carried out after a 16-year-old pupil contracted the virus.
The child was infected by her parent who had travelled overseas.
Dozens of pupils at the school were tested for coronavirus last Thursday after the case was reported.
Concerned parents and teachers told The National they were worried whether stricter measures such as home isolation for two weeks were required for pupils who had been in contact with the teenager.
As a precaution, all three schools run by the Indian High School Group closed a day early on March 5, though spring break commenced at UAE's schools and universities on March 8.
"A thorough deep clean and disinfecting has been done and the school is following proper health and safety precautions as instructed by the Ministry of Health and Prevention, Dubai Municipality and Dubai Health Authority. All necessary measures have been taken to ensure the safety of our students and staff," the school said in a statement.
"With a lot being said about the epidemic – Coronavirus or Covid-19, we understand your family members and you may have concerns and queries about the safety of your child.
“We assure you that [our] schools are following all the necessary health and safety precautions instructed by the relevant authorities.
“We have taken all the necessary measures to ensure safety of all."
The school cancelled all exams scheduled from March 5, to avoid panic among pupils and parents.
“We took this necessary step to ensure no one feels vulnerable about misleading messages circulating on social media,” it said.
Board examinations for grade 10 and 12 have not been cancelled and would go ahead as scheduled.
No re-examinations will be conducted as internal examinations have been cancelled.
Pupils will be graded and promoted on a pro rata basis.
Their portfolio, and performance in assessments and enrichment activities, will also be assessed.
After the case of the Indian High School, a 17-year-old male Emirati pupil, who showed no symptoms, also tested positive for Covid-19 on March 6.
It is not known which school the pupil goes to.
Schools and universities across the country have been closed for a month from March 8 as part of efforts to contain the spread of coronavirus.
Spring break, which was due to begin on March 29, will instead begin on March 8 and last two weeks.
Distance learning has been introduced during the remaining two weeks, with pupils learning from home.
Government schools will run a home-teaching programme called Learn from Afar from March 22 to April 5.
Private schools have set up their own distance-learning programmes or expanded existing e-learning tools such as Google Classroom, ClassDojo and Seesaw, to cover the school day.
A "sterilisation programme" for all educational facilities will be carried out in all schools, buses and universities during the break, as per the directives of the Ministry of Education in the UAE.