The 45-year-old man was arrested on Friday morning and remains in custody in Melksham, Wiltshire.
Police said in a statement that shortly before 5pm yesterday, alarms at the cathedral were activated following an attempt to smash the glass box surrounding the Magna Carta.
The man matching the description given by witnesses was arrested on suspicion of attempted theft, possession of an offensive weapon and criminal damage.
Only four known copies of the document exist, with the version held at Salisbury considered by historians to be the best-preserved.
The Magna Carta wasn't damaged and no one was injured in the incident.
Police are appealing for any witnesses who haven't already spoken to them to get in touch via 101 and quote crime reference number 541800101438.
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