Several SU UMa-type dwarf novae, in particular, WZ Sge-type stars tend to exhibit rebrightenings after superoutbursts. The rebrightening phenomenon is problematic for the disk instability theory of dwarf novae since it requires a large amount of remnant matter in the disk even after superoutbursts. Here, we report our optical and infrared observations during the first-ever outburst of a new dwarf nova, SDSS J102146.44+234926.3. During the outburst, we detected superhumps with a period of 0.056281 +/- 0.000015 d, which is typical for superhump periods in WZ Sge stars. In conjunction with the appearance of a long-lived rebrightening, we conclude that the object is a new member of WZ Sge stars. Our observations, furthermore, revealed infrared behaviors for the first time in the rebrightening phase of WZ Sge stars. We discovered prominent infrared superhumps. We calculate the color temperature of the infrared superhump source to be 4600-6400 K. These temperatures are too low to be explained with a fully-ionized disk appearing during dwarf nova outbursts. We also found a Ks-band excess over the hot disk component. These unprecedented infrared activities provide evidence for the presence of mass reservoir at the outermost part of the accretion disk. We propose that a moderately high mass-accretion rate at this infrared active region leads to the long-lived rebrightening observed in SDSS J102146.44+234926.3.