In the simplest picture, a “self-trapped” polaron forms when an excess electron or hole deforms a crystal lattice, creating a potential well with bound states. Properties of self-trapped polarons in methylammonium lead iodide perovskite (MAPbI3), which is widely used as solar cell absorber, are of great interest, and are a subject of ongoing investigations and debates concerning the existence of large polarons with the co-presence of metastable self-trapping. Herein, we employ a self-interaction-free density functional theory method to investigate the stability of small polarons in tetragonal MAPbI3 phase. The electron small polaron is found to be unstable, while the hole small polaron is found to be metastable at realistic operation temperatures of solar cells. Further, the hole polaron is found to have a hole band close to the conduction band, which in conjunction with its metastability suggests that small polarons will have an appreciable effect on charge-carrier recombinations in MAPbI3. Further, we posit that the existence of the metastable polarons in addition to the large polarons may explain the experimentally observed non-monotonic temperature dependence of bimolecular charge-carrier recombination rate in tetragonal MAPbI3 phase.