A search for Higgs boson (
H
) production in association with two vector bosons (
V
=
W
,
Z
) via vector-boson scattering (VBS) is presented using proton-proton collision data collected at
s
=
13
TeV
by the CMS experiment, corresponding to an integrated luminosity of
138
fb
−
1
. Events containing two forward jets consistent with VBS, a large-radius jet from the decay of a boosted
H
to a pair of
b
quarks, and zero, one, or two charged leptons coming from
V
decays are selected. The process is excluded at 95% confidence level for observed (expected) values of the
V
V
H
H
coupling modifier
κ
2
V
outside the interval
0.40
<
κ
2
V
<
1.60
(
0.34
<
κ
2
V
<
1.66
), assuming standard model values for all other couplings, thus establishing a novel probe of the
V
V
H
H
interaction. Constraints are also set on the individual
κ
2
W
and
κ
2
Z
coupling modifiers and on the allowed region in the
κ
2
W
−
κ
2
Z
plane.
