The first evidence of electroweak (EW) production of pairs of
Z
bosons in association with two jets (jj) in the final state
Z
Z
jj
→
ℓ
ℓ
ν
ν
jj
, where
ℓ
=
e
,
μ
, is reported by the CMS experiment. The analysis is based on a data sample of proton-proton (
p
p
) collisions at
s
=
13
TeV
, corresponding to an integrated luminosity of
138
fb
−
1
. Events are selected by requiring exactly two leptons of same flavor and opposite charge, large missing transverse momentum, and two jets with a large rapidity separation and large invariant mass. The EW production cross section in a fiducial volume is
σ
EW
(
p
p
→
Z
Z
jj
→
ℓ
ℓ
ν
ν
jj
)
=
0.3
7
−
0.12
+
0.14
(
stat
)
−
0.06
+
0.06
(
syst
)
fb
, in agreement with the standard model prediction of
0.39
±
0.06
fb
. The observed (expected) significance of the signal is 3.1 (2.8) standard deviations. Limits on anomalous quartic gauge couplings are derived in terms of dimension-8 effective field theory operators. A combination with the previously reported result from the
Z
Z
decay channel with four charged leptons yields an observed (expected) significance of 5.0 (4.5) standard deviations for the EW production of
Z
boson pairs.