The body of a 62-year-old man was discovered by police after they received a report of concern for a person at 10.30pm on November 15.
Parents were sent a text message at 6am on Tuesday telling them that the school was closed and that nobody should attend.
The school will also be closed on Wednesday.
The force has said the death is not being treated as suspicious.
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Leith Walk Primary School closed due to police incident