Not long at all — you can cover the full island in much less than a day of daytime driving, including stops to take photos, have lunch, etc. Mykonos is a fairly small island.
Is 1 day enough for Mykonos?
While it would be ideal to have more time to explore Mykonos, a one-day itinerary can still allow you to appreciate the island's highlights and get a taste of its beauty and culture.
Should I spend more days in Santorini or Mykonos?
Santorini has more tours, sightseeing, and activities: excavation sites to explore, day trips to traditional villages around the island, winery tours, and boat tours around the volcano. Mykonos has some fine scenery, beautiful walks, and picturesque windmills – but in general, Santorini has more to see and do.