Axion-like particles (ALPs) are pseudoscalar bosons predicted by string theory. The ALPs have a shallower potential than a quadratic one, which induces the instability and can form the solitonic object called oscillon/I-ball. Although the lifetime of oscillons can be very long for some type of potentials, they finally decay until the present. We perform the numerical lattice simulations to investigate the decay process of oscillons and evaluate the averaged momentum of ALPs emitted from the oscillon decay. It is found that, if oscillons decay in the early universe, the free-streaming length of ALPs becomes too long to explain the small-scale observations of the matter power spectrum. We show that oscillons with long lifetimes can change the density fluctuations on small scales, which leads to stringent constraints on the ALP mass and the oscillon lifetime.