Some things need to be at least at a certain minimum distance before they can be used at all, or are incapable of doing anything below that distance. Such as artillery not being able to fire in the first 50 meters around it.
The first video game about Minimum range was released in 1998.
In other instances this may be simply self-preservation mechanic where units or weapons refuse to fire if it would hurt themselves or their wielders due to explosions or such. Having mentioned that, this tag is not about minimum safe distance.