Health insurance is not compulsory in Italy. EU citizens can access emergency healthcare through the national health system by presenting their European Health Insurance Card. However, if your stay in Italy longer than 3 months, we advise transferring your national health insurance to the Italian Health Service (SSN) to take advantage of Italian public healthcare like an Italian citizen. To do so, you should go to the ATS, the competent local health office for your residency area in Milan. You should bring with you: 

•    S1 form – issued by the competent authority in your home country. 
•    Valid ID card 
•    Tax code – codice fiscale 

In case you do not have a S1 form, you can still obtain health insurance in Italy by voluntary subscription - "iscrizione volontaria al SSN". Voluntary subscription for students costs € 700 per calendar year (January to December). 
You may find here the list of the local ATS offices in Milan. 
You can find the complete and detailed procedure here.  
If you need extra support on this and other administrative procedures, you can contact YES Milano, an organization of the City of Milan that assists international students during their stay here. You can set up a one-to-one appointment at their One-Stop-Shop. For more info, visit their website: Welcome, Students! | YesMilano. 
 
You can check the website of the European Commission for more information. 
 

You must bring proof of internationally valid health insurance coverage, effective for the same duration as your Visa term, to the Italian Embassy or Consulate when applying for your Student Visa. 
If you do not have existing internationally valid health insurance, several private providers offer qualifying coverage for Italy that can be applied for and obtained in your home country. 
Other private providers that offer supplemental insurance include Welcome Association Italy (“WAI”), which primarily covers emergency care. 

You can find out more information about WAI here. 
     
Even if you already have private insurance, you can register with the National Health Service (“Servizio Sanitario Nazionale,” aka “SSN”) too upon arrival in Milan. Registering with the SSN is warmly suggested because it entitles international students to the same treatment as Italian citizens. Voluntary subscription for students costs € 700 per calendar year (January to December). Please note that if you enroll in September, you should purchase private health insurance for 12 months first, and then you can subscribe to the SSN.  
To register, you should go to the ATS, the competent local health office for your residency area in Milan. You should bring with you: 

•    self-certificate of enrolment at Università Cattolica (downloadable from iCatt). 
•    residence permit, or residence permit application receipt. 
•    Tax code (codice fiscale). 
•    Valid copy of your passport. 
•    receipt of the payment for the SSN subscription (see paragraph below on the Bollettino Postale). 
 
You may find here the list of the local ATS offices in Milan. 

Bollettino Postale: You can obtain it at any post office. The payment must be made on the postal account 379222 in the name of (a favore di) P.T. REGIONE LOMBARDIA and the reason for payment (causale) is “iscrizione al SSN anno… (write the year of coverage). 

If you need extra support on this and other administrative procedures, you can contact YES Milano, an organization of the City of Milan that assists international students during their stay here. You can set up a one-to-one appointment at their One-Stop-Shop. For more info, visit their website: Welcome, Students! | YesMilano.