Herein we examined the catalytic activity of the copper silicate material SGU-29 for the aerobic partial oxidation of cyclohexene under mild conditions (1 bar of O2 at 70 °C). In particular, the catalytic properties of the active sites provided by [CuO4] square planar units in SGU-29 were investigated for cyclohexene oxidation to generate three main oxidation products (i.e., 2-cyclohexene-1-ol, 2-cyclohexene-1-one, and cyclohexene hydroperoxide). Based on the molecular sieving effect of SGU-29, we especially investigated the intrazeolitic reaction, a catalytic cyclohexene oxidation occurring only in nanochannels of SGU-29. A conversion yield of 42% was obtained for the aerobic cyclohexene oxidation occurring only in SGU-29 nanochannels under 1 bar of O2 at 70 °C for 12 h. We demonstrated unequivocally that catalysis occurred only within the inner channels of SGU-29, rather than on its external surface or within the solvent, and we highlighted the special role of [CuO4] square planar units in catalysis.