After the grace period, vaccinated pupils over 12 will be tested every month, as will schoolchildren between 3 and 12 who have not been inoculated.
Saliva tests, rather than PCR swabs, have been used on younger children in recent months.
Dubai's private schools, which have their own school regulator, are not thought to be affected by the decision.
At a briefing on Sunday, Dr Farida Al Hosani, the federal government's health spokeswoman, urged “all children aged 3 to 17 to get the vaccine”.
She advised parents to arrange for their children to get vaccinated in the coming weeks.
“It is very important we prepare all pupils to attend classes face to face to ensure their education,” she said.
Despite that, Dr Al Hosani said distance learning remains an option for “all vaccinated and unvaccinated pupils".
The 30-day grace period would give families until the end of September for their children to get both shots. During that time, all unvaccinated pupils will undergo a test every two weeks.
The Pfizer-BioNTech vaccine is available for over 12s.
Al Hosn app for school pupils
The National Emergency Crisis and Disasters Management Authority detailed the latest developments on Twitter on Sunday.
Parents were asked to download the Al Hosn testing app for their children to ensure schools can see proof of vaccination and regular testing.
The app has become central to Abu Dhabi's vaccine and testing regime, including the latest rules introduced on August 20, and has seen some use in airports and bars and clubs in other emirates.
Parents will be required to print out and present PCR and vaccination certificates, in addition to downloading the app.
Dr Al Hosani said a task force of inspectors will monitor the back-to-school process and testing and vaccine requirements. Schools are required to keep social distancing of one metre and to have an isolation room for suspected cases.
She further said 86 per cent of teachers were now vaccinated and that the government was “working to reach 100 per cent very soon”. About 73 per cent of the overall population is vaccinated, the most recent figures show.
Children and teachers will be required to sign a form stating that have not knowingly been in recent contact with someone with the virus.
Masks must to be worn in all public places, including classrooms and should only be removed when eating.
She thanked schools across the country and said staff and teachers were “heroes” who had ensured children had not fallen behind in the past 18 months.
“The experience of distance learning proved to be successful despite the pandemic,” she said.
“We extend our deepest thanks for all of the heroes working on the front lines of education ... and start the new academic year by stressing the importance of all of the achievements in the past year.”
In September 2020, schools in most of the emirates reopened. But many returned to distance learning, or a hybrid model, at various times throughout the year as individual cases were detected.
At the end of the term 2021, for example, about half of pupils in Dubai were back in class, the authorities said, with the remainder learning from home.
Following a flurry of vaccinations among young people late last term, schools hope the vast majority will return to face-to-face learning once again soon.