  Confinement is an intriguing phenomenon prevalent in condensed matter and
high-energy physics. Exploring its effect on the far-from-equilibrium
criticality of quantum many-body systems is of great interest both from a
fundamental and technological point of view. Here, we employ large-scale
uniform matrix product state calculations to show that a qualitative change in
the type of dynamical quantum phase transitions (DQPTs) accompanies the
confinement-deconfinement transition in three paradigmatic models -- the
power-law interacting quantum Ising chain, the two-dimensional quantum Ising
model, and the spin-$S$ $\mathrm{U}(1)$ quantum link model. By tuning a
confining parameter in these models, it is found that \textit{branch}
(\textit{manifold}) DQPTs arise as a signature of (de)confinement. Whereas
manifold DQPTs are associated with a sign change of the order parameter, their
branch counterparts are not, but rather occur even when the order parameter
exhibits considerably constrained dynamics. Our conclusions can be tested in
modern quantum-simulation platforms, such as ion-trap setups and cold-atom
experiments of gauge theories.
