Modern cosmology has now emerged as a testing ground for theories beyond the standard model of particle physics. In this paper, we consider quantum fluctuations of the inflaton scalar field on certain noncommutative spacetimes and look for noncommutative corrections in the cosmic microwave background (CMB) radiation. Inhomogeneities in the distribution of large scale structure and anisotropies in the CMB radiation can carry traces of noncommutativity of the early universe. We show that its power spectrum becomes direction-dependent when spacetime is noncommutative. (The effects due to noncommutativity can be observed experimentally in the distribution of large scale structure of matter as well.) Furthermore, we have shown that the probability distribution determining the temperature fluctuations is not Gaussian for noncommutative spacetimes.