We suggest a quantum simulator that allows to study the
role of memory effects in the dynamics of open quantum
systems. A particular feature of our simulator is the
ability to engineer both Markovian and non-Markovian 
dynamics by means of quantum measurements and the 
quantum Zeno dynamics induced by them. The simulator is
realized by two subsystems of a bipartite quantum 
system or two subspaces of a single system which can be
identified as system and meter. Exploiting the analogy
between dissipation and quantum measurements, the 
interaction between system and meter gives rise to 
quantum Zeno dynamics, and the dissipation strength 
experienced by the system can be tuned by changing the
parameters of the measurement, i.e., the interaction 
with the meter. Our proposal can readily be realized
with existing experimental technology, such as cavity-
or circuit-QED platforms or ultracold atoms.