  A $q$-analogue of $r$-Whitney numbers of the second kind, denoted by
$W_{m,r}[n,k]_q$, is defined by means of a triangular recurrence relation. In
this paper, several fundamental properties for the $q$-analogue are established
including other forms of recurrence relations, explicit formulas and generating
functions. Moreover, a kind of Hankel transform for $W_{m,r}[n,k]_q$ is
obtained.
