Simplicial complexes successfully resolve the limitation of social networks to describe the spread of infectious diseases in group interactions. However, the effects of quarantines in the context of group interactions remain largely unaddressed. In this article, we therefore propose a susceptible-infectious-quarantine-recovered-susceptible (SIQRS) model with quarantines and study its evolution on simplicial complexes. In the model, a fraction of infected individuals is subject to quarantine, but individuals leaving quarantine may still be contagious. Using mean-field (MF) methods, we derive the propagation threshold and the steady state infection densities as well as conditions for their stability. Numerical simulations moreover show that longer quarantine times and higher quarantine ratios tend to disrupt discontinuous phase transition and bistable phenomena that are commonly due to group interactions. Additionally, when epidemic outbreaks are recurrent, although quarantine measures can reduce the peak of the first wave and delay the onset of future waves, they may also lead to an increase in subsequent peak infected densities. This highlights the need to prepare sufficient resources to deal with periodic infections after the initial wave is over.