Previous radio observations revealed widespread gas-phase methanol (CH$_3$OH) in the Central Molecular Zone (CMZ) at the Galactic center (GC), but its origin remains unclear. Here, we report the discovery of CH$_3$OH ice toward a star in the CMZ, based on a Subaru $3.4$-$4.0 mu$m spectrum, aided by NASA/IRTF $L$ imaging and $2$-$4 mu$m spectra. The star lies $sim8000$ au away in projection from a massive young stellar object (MYSO). Its observed high CH$_3$OH ice abundance ($17%pm3%$ relative to H$_2$O ice) suggests that the $3.535 mu$m CH$_3$OH ice absorption likely arises in the MYSOs extended envelope. However, it is also possible that CH$_3$OH ice forms with a higher abundance in dense clouds within the CMZ, compared to within the disk. Either way, our result implies that gas-phase CH$_3$OH in the CMZ can be largely produced by desorption from icy grains. The high solid CH$_3$OH abundance confirms the prominent $15.4 mu$m shoulder absorption observed toward GC MYSOs arises from CO$_2$ ice mixed with CH$_3$OH.
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