It may not depending on the aspect ratio of the tyre you are fitting.
You need to look at the current tyre size, and compare it the tyres and rims you are going to fit. It will be something like 215/50/R17, where the 50 represents the aspect ratio of the tyre. This is the important figure here as it defines how high the tyre wall is, and ultimately the rolling circumference of the tyre. If you are fitting a smaller rim size then the aspect ratio of the tyre will need to be larger to get the same rolling circumference. If it is, xxx/60/R16 then the rolling circumference is probably quite close. It's fairly easy on the internet to put in your tyre sizes and it will tell you the approximate rolling circumference.
If its a long way out then this will effect the speedo accuracy (it will read too high on the smaller tyre), the speed of the vehicle, and the recorded mileage.