  Let $V$ be an $n$-dimensional vector space ($4\le n <\infty$) and let
${\mathcal G}_{k}(V)$ be the Grassmannian formed by all $k$-dimensional
subspaces of $V$. The corresponding Grassmann graph will be denoted by
$\Gamma_{k}(V)$. We describe all isometric embeddings of Johnson graphs
$J(l,m)$, $1<m<l-1$ in $\Gamma_{k}(V)$, $1<k<n-1$ (Theorem 4). As a
consequence, we get the following: the image of every isometric embedding of
$J(n,k)$ in $\Gamma_{k}(V)$ is an apartment of ${\mathcal G}_{k}(V)$ if and
only if $n=2k$. Our second result (Theorem 5) is a classification of rigid
isometric embeddings of Johnson graphs in $\Gamma_{k}(V)$, $1<k<n-1$.
