Studies of young stellar objects (YSOs) in the Galaxy have found that a significant fraction exhibit photometric variability. However, no systematic investigation has been conducted on the variability of extragalactic YSOs. Here we present the first variability study of massive YSOs in a $sim 1.5,mathrm{deg^2}$ region of the Large Magellanic Cloud (LMC). The aim is to investigate whether the different environmental conditions in the metal-poor LMC ($sim$ 0.4-0.5 Z_sun) have an impact on the variability characteristics. Multi-epoch near-infrared (NIR) photometry was obtained from the VISTA Survey of the Magellanic Clouds (VMC) and our own monitoring campaign using the VISTA telescope. By applying a reduced $chi^2$-analysis, stellar variability was identified. We found 3062 candidate variable stars from a population of 362 425 stars detected. Based on several Spitzer studies, we compiled a sample of high-reliability massive YSOs: a total of 173 massive YSOs have NIR counterparts ($K_{mathrm{s}}sim 18.5,$mag) in the VMC catalogue, of which 39 display significant ($>3sigma$) variability. They have been classified as eruptive, fader, dipper, short-term variable and long-period variable YSOs based mostly on the appearance of their $K_{mathrm{s}}$ band light curves. The majority of YSOs are aperiodic, only five YSOs exhibit periodic lightcurves. The observed amplitudes are comparable or smaller than those for Galactic YSOs (only two Magellanic YSOs exhibit $Delta K_{mathrm{s}}>1,$mag), not what would have been expected from the typically larger mass accretion rates observed in the Magellanic Clouds.
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