  Let $G$ be a finite simple graph with vertex set $V(G)$ and edge set $E(G)$.
A function $f : V(G) \rightarrow \mathcal{P}(\{1, 2, \dotsc, k\})$ is a
\textit{$k$-rainbow dominating function} on $G$ if for each vertex $v \in V(G)$
for which $f(v)= \emptyset$, it holds that $\bigcup_{u \in N(v)}f(u) = \{1, 2,
\dotsc, k\}$. The weight of a $k$-rainbow dominating function is the value
$\sum_{v \in V(G)}|f(v)|$. The \textit{$k$-rainbow domination number}
$\gamma_{rk}(G)$ is the minimum weight of a $k$-rainbow dominating function on
$G$. In this paper, we initiate the study of $k$-rainbow domination numbers in
middle graphs. We define the concept of a middle $k$-rainbow dominating
function, obtain some bounds related to it and determine the middle $3$-rainbow
domination number of some classes of graphs. We also provide upper and lower
bounds for the middle $3$-rainbow domination number of trees in terms of the
matching number. In addition, we determine the $3$-rainbow domatic number for
the middle graph of paths and cycles.
