Yup, totally unprofessional and in many cases consideration for constructive dismissal - in that he expects you to find out and resign, saving the company the trouble of firing you or his personal preference to get rid of you without any means of firing you.
So, start keeping a diary of all the times he has been like this, all the things you've heard or been told. Then go to HR with this evidence (even if it feels circumstantial and hearsay to you) and demand something be done to stop it now, and stop it in the future. Take someone with you to act as a witness, and HR will understand you are serious (and they also give you "got your back" support that really helps deal with a HR who will want you to just go away and stop giving them a hard time)
HR will instantly recognise this as a serious legal problem for them, and their job of protecting the company will ensure they deal with it (this applies even if you have no intention of going down the legal sue-the-company route, just leave that hint hanging)
Working in a place where your manage is undermining you will cause a great deal of stress, you don't need that. Don't think it'll sort itself out, it'll only get worse if unchecked.