Causeway Coast and Glens Borough Council told Premier it was looking into the matter.
The rag tree is at Dungiven Priory, the remains of an 11-century Augustinian dwelling for monks.
Over the years people have been praying at the tree and tying rags there to symbolise leaving their prayer in God's hands.
Some believe washing a wart with the rag, then tying the rag to a tree, will cure the wart. It relates to a small well by the tree called Wartwell.
The practice is similar to praying and lighting a candle in church.
Archaeologist Nick Brannon told the Belfast Telegraph: "I was so angry when I saw the tree bare because I thought of all of the people over decades and decades who would have come to this special place and prayed and tied a rag to the tree.
"I do know this wasn't an act of random vandalism because the rags were taken from the tree, they weren't left scattered around, so a lot of time and effort went into this."
A spokesman said: "Causeway Coast and Glens Borough Council can confirm that none of its staff were responsible for removing the rags.
"Council's maintenance squad, grass cutting squad and hedge cutter are aware of the tree and would have no reason to remove or touch any of the rags."
