  We study the constraints on possible new physics contribution to the
forward-backward asymmetry of muons, A_{FB}(q^2), in B --> K mu+ mu-. New
physics in the form of vector/axial-vector operators does not contribute to
A_{FB}(q^2) whereas new physics in the form of scalar/pseudoscalar operators
can enhance A_{FB}(q^2) only by a few per cent. However new physics the form of
tensor operators can take the peak value of A_{FB}(q^2) to as high as 40% near
the high-q^2 end point. In addition, if both scalar/pseudoscalar and tensor
operators are present, then A_{FB}(q^2) can be more than 15% for the entire
high-q^2 region q^2 > 15 GeV^2. The observation of significant A_{FB} would
imply the presence of new physics tensor operators, whereas its q^2 dependence
could further indicate the presence of new scalar/pseudoscalar physics.
