The Micromegas is a type of ionising radiation detector that consists of a gas chamber sandwiched between two parallel plate electrodes, with the gas chamber divided by a Frisch grid into drift and amplification gaps. Investigators have applied it to a number of different applications, such as charged particle, X-ray and neutron detection. A Micromegas device has been tested as a neutron beam monitor at CERN and is expected to be used for that purpose at the Spallation Neutron Source (SNS) under construction in Oak Ridge, TN. For the Micromegas to function effectively as neutron beam monitor, it should cause minimal disruption to the neutron beam in question. Specifically, it should scatter as few neutrons as possible and avoid neutron absorption when it does not contribute to generating useful information concerning the neutron beam. Here, we present the results of Monte Carlo calculations of the effect of different types of wall materials and detector gases on neutron beams and suggest methods for minimising disruption to the beam.