  Using a functional renormalization group approach we derive the
renormalization group (RG) flow of a dissipative variant of the
Yukawa-Sachdev-Ye-Kitaev model describing $N$ fermions on a quantum dot which
interact via a disorder-induced Yukawa coupling with $M$ bosons. The inverse
Euclidean propagator of the bosons is assumed to exhibit a non-analytic term
proportional to the modulus of the Matsubara frequency. We show that, to
leading order in $1/N$ and $1/M$, the hierarchy of formally exact flow
equations for the irreducible vertices of the disorder-averaged model can be
closed at the level of the two-point vertices. We find that the RG flow
exhibits a non-Fermi liquid fixed point characterized by a finite fermionic
anomalous dimension $\eta$ which is related to the bosonic anomalous dimension
$\gamma$ via the scaling law $2 = 2 \eta + \gamma$ with $ 0 < \eta < 1/2$. We
explicitly calculate $\eta$ and the critical exponents characterizing the
linearized RG flow in the vicinity of the fixed point as functions of $N/M$.
