Lewisham Council said teachers at Crofton School, Lewisham, first became suspicious that somebody was entering the school out of hours in December.
On Monday they caught sight of the man after they heard him moving around.
The south-east London school will be shut until next week. Year 11 students will study for their GCSEs in a building the man has not accessed.
"Closure will allow us to carry out a systematic search of the site with the police to ensure it remains secure"
A Lewisham Council spokesman said the man is not thought to pose a direct threat to children and added that nothing had been stolen from the school.
He added that the only description they have of the man is that he is black.
A private security firm will give 24-hour cover to the site while police look for the man.
A spokesman for the school said: "We take the safety of our pupils and staff extremely seriously.
"Our decision to close the school has come as part of escalating and on-going efforts to bring this matter to a conclusion.
"Closure will allow us to carry out a systematic search of the site with the police to ensure it remains secure."
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