Let $(\mathcal{X}, d, \mu )$
(
X
,
d
,
μ
)
be a non-homogeneous metric measure space, which satisfies the geometrically doubling condition and the upper doubling condition. In this paper, the authors prove the boundedness in $L^{p} (\mu )$
L
p
(
μ
)
of mth-order commutators $\mathcal{M}^{\rho }_{b,m}$
M
b
,
m
ρ
generated by the Log-Dini-type parametric Marcinkiewicz integral operators with RBMO functions on $(\mathcal{X}, d, \mu )$
(
X
,
d
,
μ
)
. In addition, the boundedness of the mth-order commutators $\mathcal{M}^{\rho }_{b,m}$
M
b
,
m
ρ
on Morrey spaces $M^{q}_{p}(\mu )$
M
p
q
(
μ
)
, $1< p \leq q< \infty $
1
<
p
≤
q
<
∞
, is also obtained for the parameter $0<\rho <\infty $
0
<
ρ
<
∞
.