Birmingham City Council sought the injunction after months of protests outside Anderton Park Primary School.
The council said it pursued the legal action after perceived risks to children became “too serious to tolerate”.
It also said the behaviour of the peaceful protesters was “increasingly unacceptable”.
The local authority said it submitted the application to protect pupils and staff when they return from their half-term break on Monday 3 June.
Demonstrators were not informed of the High Court application but told 5Pillars they still plan to gather next week on a street further away from the school.
The injunction will be in place until Monday 10 June, when the parents who are opposing the pro-LGTB lessons will be able to present their case in front of a judge.
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The exclusion zone covers the streets surrounding the school, which sits on Dennis Road, from Taunton Road, Birchwood and Yardley Lane.
Muslim parents started protesting over concerns their children were “too young” to be “indoctrinated” about LGBT relationships, which they say contradicts Islamic morals, values and ethics.