  We elucidate how the presence of higher-form symmetries affects the dynamics
of thermalization in isolated quantum systems. Under reasonable assumptions, we
analytically show that a $p$-form symmetry in a $(d+1)$-dimensional quantum
field theory leads to the breakdown of the eigenstate thermalization hypothesis
for many nontrivial $(d-p)$-dimensional observables. For higher-form (i.e.,
$p\geq 1$) symmetry, this indicates the absence of thermalization for
observables that are non-local but much smaller than the whole system size. We
numerically demonstrate this argument for the (2+1)-dimensional $\mathbb{Z}_2$
lattice gauge theory. While local observables such as the plaquette operator
thermalize, the non-local observable exciting a magnetic dipole instead relaxes
to the generalized Gibbs ensemble that takes account of the $\mathbb{Z}_2$
1-form symmetry.
