Mine did that as well. It freaked me out. we stopped the bottle feeding and transitioned to mash (kibbles soaked in warm formula-like oatmeal). She was about 6 weeks old anyways so it was about time.
Depending on the size he swallowed it could cause a blockage. Before you panic too much consider: Is kitty vomiting/coughing ? Has he taken a poop normally since then? Acting lethargic? If you suspect something is wrong the vet can do an xray to identify where the nipple piece is. If it’s causing a blockage, surgery may be necessary.
In my case, she acted normally. I checked her poop and she had passed it the next day.
If it's just a small piece, chances are it will pass and be OK. If it's a big piece, it may stay stuck in their stomach. If there is any vomiting/diarrhea, lethargy, crying, or not eating or using the litter box, definitely go to the vet ASAP. My (adult) cat ate one of those big purple rubber bands they use to tie broccoli together in the grocery store and after a $500 vet bill and x-rays he pooped it out the minute we got home.