I have a niece who did this and my clueless sister didn't think much of it....so I opened up my nighty drawer one night and handed her an old silky pajama top (which was from an old boyfriend, so it was time to pass it along). She instantly bonded to the silky, soft feeling of the fabric. She carried that silky with her everywhere for quite a few years until it was cut up into little squares and she could keep them in different places. She just needed something silky to nuzzle.
And if the redirecting doesn't work, I would recommend an adorable short hair cut, not a buzz...just enough where she can't keep her arm in a comfortable position while she's trying to pull it towards her mouth.