Source: Apple
Best answer: Unfortunately, no, your old case won't fit the iPhone 12 mini. The iPhone 12 mini is a completely new size of iPhone, and as such, it needs brand new cases.
The standard Apple case: Apple Silicone case with MagSafe for iPhone 12 ($49 at Apple)
The iPhone 12 mini is a brand new size all around
Not only does the iPhone 12 mini sport a brand new screen size, 5.4 inches, but it does see the introductions of a new body size, too. The iPhone 12 mini is the smallest flagship iPhone that Apple has made since the iPhone 5s, though it isn't quite that small.
There's also the matter of the new design on the iPhone 12 series of phones. Even if the iPhone 12 mini were the size of an existing iPhone, the new design would preclude it from working with existing cases.
Apple's got a brand new set of cases, and they're magnetized
One of the key components of the iPhone 12 lineup is MagSafe. MagSafe is a magnetic accessory and charger connection on the back of the new iPhones, including the iPhone 12 mini. All of Apple's first-party cases, including the silicone, clear, and the upcoming leather options, come with MagSafe magnets inside.
Not only do these MagSafe cases allow you to connect magnetic accessories to your iPhone while using a case, but they also let your iPhone charge through the MagSafe charger while in a case. Of course, you can connect to these accessories and the charger without a case, too.
And if you don't like any of Apple's options, there are some great iPhone 12 mini cases already available to order.
The Apple default case

Apple Silicone case with MagSafe for iPhone 12
Apple's standard silicone case, this time, with MagSafe.
This year, all of Apple's first-party cases come equipped with MagSafe, so you don't have to worry about getting the right version. The iPhone 12 mini version of its silicone case features a beautiful set of new colors and will protect your iPhone against most common drops.
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