The Vista Variables in the Via Lactea (VVV) survey has allowed for an unprecedented number of multi-epoch observations of the southern Galactic plane. In a recent paper, 13 massive young stellar objects (MYSOs) have already been identified within the highly variable (ΔK_s > 1 mag) YSO sample of another published work. This study aims to understand the general nature of variability in MYSOs. Here we present the first systematic study of variability in a large sample of candidate MYSOs. We examined the data for variability of the putative driving sources of all known Spitzer extended green objects (EGOs; 270) and bright 24 μm sources coinciding with the peak of 870 μm detected ATLASGAL clumps (448), a total of 718 targets. Of these, 190 point sources (139 EGOs and 51 non-EGOs) displayed variability (IQR > 0.05, ΔK_s > 0.15 mag). 111 and 79 light-curves were classified as periodic and aperiodic respectively. Light-curves have been sub-classified into eruptive, dipper, fader, short-term-variable and long-period-variable-YSO categories. Lomb-Scargle periodogram analysis of periodic light-curves was carried out. 1–870 μm spectral energy distributions of all the variable sources were fitted with YSO models to obtain the representative properties of the variable sources. 41% of the variable sources are represented by > 4 M_⊙ objects, and only 6% were modelled as > 8 M_⊙ objects. The highest-mass objects are mostly non-EGOs, and deeply embedded, as indicated by nearly twice the extinction when compared with EGO sources. By placing them on the HR diagram we show that most of the lower mass, EGO type objects are concentrated on the putative birth-line position, while the luminous non-EGO type objects group around the zero-age-main-sequence track. Some of the most luminous far infrared (FIR) sources in the massive clumps and infrared quiet driving sources of EGOs have been missed out by this study owing to an uniform sample selection method. A high rate of detectable variability in EGO targets (139 out of 153 searched) implies that near-infrared variability in MYSOs is closely linked to the accretion phenomenon and outflow activity.