There are a few different ways that a fuse can cause a transmission not to shift. The most common way is if the fuse that controls the transmission's shifting solenoids is blown. If this happens, then the transmission will likely be stuck in one gear and won't be able to shift into any others. Another way that a blown fuse can cause problems with shifting is if it blows the fuse for the transmission's computer. This can prevent the transmission from knowing when to shift, and as a result, it may not shift at all or may shifted erratically.
Of course, there are other potential causes of a transmission not shifting properly, so if you're experiencing this problem, it's best to have it diagnosed by a professional.