It\^{o}'s theorem and monomial Brauer characters

Let $G$ be a finite solvable group, and let $p$ be a prime. In this note, we prove that $p$ does not divide $\phi (1)$ for every irreducible monomial $p$-Brauer character $\phi$ of $G$ if and only if $G$ has a normal Sylow $p$-subgroup.