Dyfed-Powys Police said the victims were being treated for injuries at Amman Valley School in Ammanford, Carmarthenshire.
Police did not disclose what happened, the nature of the injuries or why the alleged suspect was arrested.
The school was closed.
"We would ask that people do not speculate while there is a police investigation ongoing," police said in a statement.
A school governor said she had been told the incident was a stabbing, with members of staff injured.
Wales First Minister Vaughan Gething said he was "shocked to hear" about the "serious incident" while United Kingdom Prime Minister Rishi Sunak thanked police and emergency services attending the scene.
He also thanked the police and ambulance crews for their response.
David TC Davies, the Secretary of State for Wales, described an incident at a school in Ammanford as "deeply concerning".
Davies said: "The news emerging from Ammanford this afternoon is deeply concerning."
Amman Valley School, or Ysgol Dyffryn Aman, is a bilingual comprehensive school for those aged between 11 and 18.
In an interview with WalesOnline, Karen Davies - a governor at the school - said she had been told the incident involved a stabbing.
Davies said she did not know whether any children had been injured.
"I have been told someone has been arrested and that two members of staff have been stabbed but have no confirmation on how serious the injuries are," she told WalesOnline.
with PA
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