  Recent infrared (IR) observations of the center of our Galaxy indicate that
the supermassive black hole source Sgr A* is strongly variable in the IR. The
timescale for the variability, $\sim 30$ min, is comparable to that of the
X-ray flares observed by {\em Chandra} and {\em XMM}, suggesting a common
physical origin. In this paper, we investigate the nature of the IR emission in
the context of models recently proposed to interpret the X-ray flares. We show
that the IR emission in Sgr A* can be well explained by nonthermal synchrotron
emission if a small fraction of the electrons in the innermost region of the
accretion flow around the black hole are accelerated {into a broken power-law
distribution}, perhaps due to transient events such as magnetic reconnection.
The model predicts differences in the variability amplitudes of flares in the
IR and X-rays, in general agreement with observations. It also predicts that
the IR emission should be linearly polarized, as has indeed been observed
during one epoch. IR and X-ray flares analogous to those observed in Sgr A* may
be detectable from other accreting SMBHs, provided $L \lsim 10^{-8} L_{EDD}$;
at higher luminosities the flaring emission is dominated by thermal
synchrotron-self Compton emission, which is likely to be less variable.
