  We study gravitational collapse of a spherical fluid in nonrelativistic
general covariant theory of the Ho\v{r}ava-Lifshitz gravity with the
projectability condition and an arbitrary coupling constant $\lambda$, where
$|\lambda - 1|$ characterizes the deviation of the theory from general
relativity in the infrared limit. The junction conditions across the surface of
a collapsing star are derived under the (minimal) assumption that the junctions
be mathematically meaningful in terms of distribution theory. When the
collapsing star is made of a homogeneous and isotropic perfect fluid, and the
external region is described by a stationary spacetime, the problem reduces to
the matching of six independent conditions. If the perfect fluid is
pressureless (a dust fluid), it is found that the matching is also possible. In
particular, in the case $\lambda = 1$, the external spacetime is described by
the Schwarzschild (anti-) de Sitter solution written in Painlev\'e-Gullstrand
coordinates. In the case $\lambda \not= 1$, the external spacetime is static
but not asymptotically flat. Our treatment can be easily generalized to other
versions of Ho\v{r}ava-Lifshitz gravity or, more generally, to any theory of
higher-order derivative gravity.
