South Wales Police said it had worked with Bishop Vaughan School on a "sensitive safeguarding issue involving two pupils" on Wednesday.
The pupils were not at the school at the time of the arrests.
A statement on the school website said the school would not open on Thursday due to the disruption. It will reopen as normal after the Easter break.
A joint police and Swansea council statement said: "Given the confidential nature of the pupil issue, it wouldn't be appropriate for us to comment further at this time."
A Swansea school has been closed following "unusual circumstances" and the arrest of two pupils.