Fingernail Wrinkles

Hummm. You state "baby" - how young are you talking? Newborn? Baby fingernails are extremely flimsy and the "wrinkles" could be that they have not had time to strengthen. I know that wrinkles in adult fingernails are usually caused by a trauma to the nailbed, but I find that unlikely for a newborn. If you are referring to a newborn - I would give them a couple of months to harden and straighten out.

Definitely ask a doctor. I have always heard that changes to your nails can indicate a vitamin deficiency. I'm not sure about "wrinkles" ( I can't even really picture it) but I know ridges on the nails can indicate that. And the fact that they are new is strange too.

I used to babysit for a child with ridges on just her thumb nails because she was a thumb sucker. She was not a baby though, probably about 5 years old when I noticed it but it lasted years

Does the child have any skin conditions?

did the babies finger get pinched or is it all their nailbeds. If it is all the nail beds my gut thinks there is some kind of nutritional deficiency or a cardiac problem. Check with your doc. Good luck

Please don't panic after those last couple of answers. Cardiac problems...shhesh.
Baby nails are very thin. They do all kinds of strange stuff. Start with calling your pediatrician. Have you had your 6 month check up yet??? Have you changed his/her diet lately? Stopped BF of changed formula brands??? Have you added new foods yet? All these things can effect vitamin intake.
It is most likely nothing serious. Dont panic.