LinkedIn publishes this information on your profile, ready for any identity thief to pick up and use. Thanks LinkedIn!
The only way they display this information is if you (a) add it to your profile, and (b) make that information public.
If you use LinkedIn to tell people when your birthday is - and I have no idea why you would, given its intended use case - then that's your doing, not theirs.
Use this link to edit your profile:
https://www.linkedin.com/profile/edit?trk=tab_pro
In the "Additional Info" section, either set Birthday back to "Month..." and "Day..." or click on the icon next to it to reduce its visibility to only your network or connections. Then click the "Save" button.
P.S.: You can always lie about your birthdate.