It depends on how much eye candy you want to turn on. Todd said in the E3 demo that they've added volumetric lighting to the engine (which is largely responsible for how much better FO4 looks than Skyrim) and that can be very demanding.That eats frame rate quite a bit.
The specs for Skyrim's recommended settings are thus:
Intel Quad-core Processor
RAM: 4GB - 6GB
Video Card: DirectX9 video card with 1GB memory. GTX 260/Radeon 4890 or higher
That is to run Skyrim on HIGH. NOT on Ultra.
I would imagine that Skyrim's High requirements are what FO4's minimum requirements will be close to. But to run on minimum at a good framerate you are probably going to have to turn off the things that are making the demo look so good, like the the advanced lighting.
Personally I'd say for minimum, I'd go with a quad-core processor, same RAM requirements as Skyrim, and video card with at least 2GB of VRAM - probably at least a 400 series Geforce card. But it is all speculation at this point.