The Cardinal Newman School in Hove, East Sussex said it believed the drinks impaired pupils' ability to concentrate in class and behave.
Tesco said there was no law banning the sale of caffeine drinks but that it was co-operating with the store. A local newsagent has also agreed not to sell the drinks.
The school's move comes four years after the education secretary Ruth Kelly announced the government was banning vending machines selling soft drinks and snacks in schools.
A similar situation occurred in central London last year when to ban the sale of high-strength alcohol in a bid to deter anti-social behaviour.
It is the second time this week soft drinks have come under the spotlight. Earlier this week the .
The ASA said the press ads, which used the lines "Keep perky when you’re feeling murky" and "More muscles than Brussels" have banned for being ambiguous and misleading consumers about possible health benefits.
, according to researchers Mintel. The category grew by 51% between 2004 and 2008.