The scalar median filter (SMF) is often used to reduce noise in scalar geophysical data. We present an extension of the SMF to a vector median filter (VMF) for suppressing noise contained in geophysical data represented by multidimensional, multicomponent vector fields. Although the SMF can be applied to each component of a vector field individually, the VMF is applied to all components simultaneously. Like the SMF, the VMF intends to suppress random noise while preserving discontinuities in the vector fields. Preserving such discontinuities is essential for exploration geophysics because discontinuities often manifest important geologic features such as faults and stratigraphic channels. The VMF is applied to synthetic and field data sets. The results are compared to those generated by using SMF, f-x deconvolution, and mean filters. Our results indicate that the VMF can reduce noise while preserving discontinuities more effectively than the alternatives. In addition, a fast VMF algorithm is described for reducing computation time.