  We study the amplitude modulation of nonlinear kinetic Alfv{\'e}n waves
(KAWs) in an intermediate low-beta magnetoplasma. Starting from a set of fluid
equations coupled to the Maxwell's equations, we derive a coupled set of
nonlinear partial differential equations (PDEs) which govern the evolution of
KAW envelopes in the plasma. The modulational instability (MI) of such KAW
envelopes is then studied by a nonlinear Schr{\"o}dinger (NLS) equation derived
from the coupled PDEs. It is shown that the KAWs can evolve into bright
envelope solitons, or can undergo damping depending on whether the
characteristic ratio $(\alpha)$ of the Alfv{\'e}n to ion-acoustic (IA) speeds
remains above or below a critical value. The parameter $\alpha$ is also found
to shift the MI domains around the $k_xk_z$ plane, where $k_x~(k_z)$ is the KAW
number perpendicular (parallel) to the external magnetic field. The growth rate
of MI, as well as the frequency shift and the energy transfer rate, are
obtained and analyzed. The results can be useful for understanding the
existence and formation of bright and dark envelope solitons, or damping of KAW
envelopes in space plasmas, e.g., interplanetary space, solar winds etc.
