Here is a typical post talking about pineapple for this purpose. Some people say it's the bromelain in it, and some people say it's the selenium content. It's hard to find good info on this, seems like all the websites are just reporting hearsay. I originally heard about it in the book The Infertility Cure: The Ancient Chinese Wellness Program for Getting Pregnant and Having Healthy Babies (which incidentally has an excellent chapter on fibroids).
Plus, am thinking the pineapple could help the fibroids too. Bromelain is an enzyme, which reduces inflammation in the body. And perhaps like other enzymes (nattokinase, protease, serraptase, etc.) might be able to help shrink fibroids.
This page mentions pineapple specifically for fibroids, so do this one and this one and this one. Wow, a lot of people are talking about it.
Bromelain is also an ingredient in the anti-fibroid enzyme pills FibroVera and Wobenzyn. These are two of those high-priced enzyme supplements often touted on the web that I believe one can do just as well by getting the ingredients separately.
For TTC purposes, one is only supposed to do the pineapple during the week after ovulation. Before that, and it could make you too acidic which is bad for sperm. After that, and pineapple supposedly can bring on miscarriage.
If one were not TTC, then eating pineapple or taking bromelain all the time sounds like it would be a good addition to a fibroid shrinking regimen (bromelain on its own might be better as it's more concentrated and might not make you acidic the way lots of pineapple can