The doctor's sheet comes first
An apostille is one stamp a Hague country puts on a paper so another country takes it with no embassy step. It sits on a signature, so the sheet must carry one that Italy can check. If you are asking how to apostille a Medical Certificate, start with who signs it, not with where you queue. A doctor inside the public health service gives you the clean case.
Ask for the certificate in writing and keep it plain. It should name you, give the day it was written, state the finding and carry the doctor's seal. Leave out history the reader never asked about. You can only apostille a Medical Certificate in Italy when an Italian doctor or health office signed the sheet.
The desk, the fee and the wait
Papers of this kind go to the Prefettura, the prefecture. Court and notary work goes to the Procura della Repubblica instead, so this route stays on the plain side. To apostille a Medical Certificate in Milan you hand in the signed sheet, and you reckon on one stamp per paper, since each certificate counts on its own.
The apostille cost for a Medical Certificate in Milan is a €16 tax stamp per document, and some papers are exempt, so ask before you pay. Your doctor or clinic may bill you on its own terms for writing the note. Waits at the desk move with the queue, so treat any date you hear as a guess and keep days spare.
Where it goes, and the words in it
Readers abroad ask for stamped health papers for a visa or a stay permit, for a school or a sports club, for a work post, or to back an insurance claim. Each of them wants one narrow answer. Send the sheet that gives it, and ask the reader to spell out the wording they expect before your doctor writes.
The legalisation of a Medical Certificate in Milan ends with the apostille when the reader's country is in the Hague group. Health words travel badly, so most desks want the text in their own tongue as an asseverazione, a sworn translation that a court in Italy stamps. No language is fixed here, so have the reader name it in writing.