As a bare minimal, you would need to look for a GPU that explicitly states that it supports 4k resolution or higher. GTX950 would be one of them. Nvidia has a list of their supported GPUs on their website: http://www.geforce.com/hardware/technology/4k/supported-gpus.
However, this would only be if you want to be able to use the 4k monitor in normal tasks. Gaming would be a different story.
Any old decent GPU might be able to play games fairly well at 1080p with 60+fps. But 4k will necessitate that there will be 4x as many pixels being processed, which would require at least 4x as much of a pixel rate. Something like a HD6850 (going for around 35-45$ CAD on CL) plays fairly decently at 1080p with a pixel rate of 24800 Mpixels/sec. If you want similar experience to that, the GPU would have to have a pixel rate of 99200 Mpixels/sec. That would be something slightly better than a GTX980Ti.
A GTX950, with 32768 Mpixels/sec, can drive your 4k monitor, but that might mean that you would only be getting a cinematic 24fps in games.