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We present the discovery of the simultaneous flux variation of a massive young stellar object (MYSO) G036.70+00.09 (G036.70) both in the maser emission and mid-infrared (MIR;$λ=3$--$5$~$μ$m) bands. Utilizing the ALLWISE and NEOWISE archival databases covering a long time span of approximately 10 years with a cadence of 6 months, we confirmed that G036.70 indicates a stochastic year-long MIR variability with no signs of the WISE band color change of W1 (3.4~$μ$m) $-$W2 (4.6~$μ$m). Cross-matching the MIR data set with the high-cadence 6.7~GHz class II methanol maser flux using a Hitachi 32-m radio telescope that discovered its periodicity in the methanol maser of 53.0--53.2 days, we also determine the flux correlations between the two bands at two different timescales, year-long and day-long, both of which have never been reported in MYSOs except when they are in a state of the accretion burst phase. The results of our study support the scenario that a class II methanol maser is pumped up by infrared emission from accreting disks of MYSOs. We also discuss the possible origins of MIR and maser variability. To explain the two observed phenomena, a stochastic year-long MIR variability with no signs of significant color change and maser-MIR variability correlation, change in mass accretion rate and line-of-sight extinction because of nonaxisymmetric dust density distribution in a rotating accretion disk are possible origins. Observations through spectroscopic monitoring of accretion-related emission lines are essential for determining the origin of the observed variability in G036.70.