The paradigm of the neutralino dark matter predicts that the first gravitationally bound objects are Earth-mass microhalos, which would emit annihilation gamma rays. Here we show that, although the flux from individual nearest microhalos is extremely difficult to detect, meaningful constraints on their survival probability and internal density profile can be set by requiring that the Galactic and extragalactic gamma-ray background flux from the microhalos does not exceed the existing EGRET background data. Possible disruption of microhalos by stellar encounters does not significantly reduce the background flux. If the probability for microhalos to survive the hierarchical clustering process of dark matter is as large as indicated by a recent simulation, they could be a significant component of the observed background flux in some photon energy range, even with the standard annihilation cross section and the conservative internal density profile of microhalos. The integrated gamma-ray flux from microhalos in the halo of the Andromeda galaxy may also be detectable by observations in the near future.
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