Split your vector field into components (how to do this depends on how it is stored to start with). Smooth each component separately and reassemble them if necessary.
To smooth a 2-D scalar array, you can use conv2 with a suitable kernel. The choice of kernel depends on how much you want to smooth and what your smoothing requirements are. Typically a Gaussian is a good choice - if you have the Image Processing Toolbox you can use fspecial to get one.
