Photo by Tscherno (Flickr)
The answer is no but their ability to see colour is limited. The cat's retina is made up of two types of light sensitive cells; rods and cones. The rods enable the cat to see black, white and shades of grey.
The cones provide the color vision. There are many rods and few cones. The cat can see well in poor light but color vision is limited.
In fact the cat has a "reduced ability to see fine detail and a variety of colours"1. The cones that are in the retina react to light waves within the green and blue regions of the spectrum. The retina contains very few cones that are sensitive to the longer light waves such as red.
For this reason people say that the cat has "dichromatic vision" - vision in which only two of the three primary colors are perceived. The three primary colors are; blue, green and red1.
The cat's eyes are adapted for crepuscular (dawn and dusk) hunting. The cats eyes are specialized to see movement.
1. The Cat, Its Behavior, Nutrition & Health by Linda P Case.