The short answer
Eid al-Adha 2027 is expected about 16 to 17 May, though the date depends on the moon and our calendar marks it for checking. It is the year's biggest family holiday: most non-hotel restaurants and many shops close for several days, and buses and trains are packed as people travel home.
In more detail
Eid al-Adha, the Feast of the Sacrifice, falls about seventy days after Eid al-Fitr, which in 2027 is expected about 9 to 10 March. Like every Islamic date, it is confirmed only after the moon sighting, so treat 16 to 17 May as approximate and check close to your trip.
Our calendar research is blunt about the effect: it calls Eid al-Adha week a poor one for medina-focused trips. The days before are busy with families buying sheep and heading home. On the day and for several days after, the souks are half shut and local restaurants close. Riads and hotels keep serving their guests.
If your dates overlap, book airport transfers and any train or long drive early, plan meals at your riad or hotel, and consider using those days for a mountain or desert trip with a private driver. The main sights mostly stay open, and the quiet medina has its own atmosphere if you go in expecting closures.