You will be required to submit to a medical exam with a local USCIS-approved doctor (known as a Designated Civil Surgeon), before your green card application will be approved. Some of these doctors are non-Americans who reside overseas.
Your application could be denied if your examination shows that you have contracted a communicable disease. Not all communicable diseases will result in rejection of your application, however – HIV, for example, was recently removed from this list, such that you can enter and remain in the US even if you are HIV positive.