Should I Be Able to Feel the Abdominal Muscle Suture After a Tummy Tuck?

This could due to several different causes. Is your drain still in place? Do you have a seroma? Are you exceptionally thin? If it is the latter condition, it is possible that that you are feeling the suture. Some materials are more palpable than others. Discuss your symptoms with your surgeon so that they can explain the possible source. 

Rather and guessing and asking us to provide you with more scenarios to speculate about I would advise you to have your surgeon tell you what you are feeling. After all, he/she was there and knows what the object is.
IF you are thin, you MAY be feeling the knot of one of the sutures. If this is the case and the stitch is a non-dissolving / permanent suture - then you would feel it for life. If it is a dissolving suture, it will be gone in a few months. Want to find out ? ask your surgeon.

Without  the benefit of an exam, you are probably describing a suture.  In very thin women, the sutures that are used to repair the rectus muscles can sometimes be palpable, but almost never are they visible.  After you are fully healed - 6 months or so - if this still concerns you, the suture can be removed through a small incision under local.  Good luck.

It is not uncommon to feel all sorts of unusual things after a tummy tuck. Sometimes it is just a muscle band or scar, or it could be a suture. Speak to your doctor or his nurse and ask what it might be if it bothers you. He might want to see you a little earlier than your regular appointment.

It is difficult to know for sure, but it sounds as if the object that you can feel may well be the suture utilized for your muscle repair.  This would be more likely if you are especially thin. Check with your surgeon regarding this.  You may become less bothered by it with the passage of time.