We examine the effects of small-scale tangled magnetic fields on the ideal MHD collapse of an individual nonrotating cloud. For a given initial nonrotating cloud in a gravitational equilibrium, we find that the pressure of the tangled field does not inhibit the gravitational collapse once the collapse occurs at the very core. It proceeds in an inside-out fashion first pointed out by Shu (1977) for unmagnetized low-mass clouds. We present a scenario as to how such small-scale magnetic fields may arise, during a sequence of contraction processes in a diffuse cloud permeated by a large-scale interstellar magnetic field. The scenario is built upon the well-established model (Mouschovias 1977), where the original cloud is contracting along the large-scale field to form a pancake configuration. Relatively weak small-scale fields in the original diffuse cloud are then amplified in the process of contraction, as a result of compression into the disk. When the disk becomes gravitationally unstable after a long period of redistribution of magnetic fields by the ambipolar diffusion, clumps of almost spherical shape will be formed. This subsequently sets up the initial condition for the spherical collapse. We derive a condition for the compressed cloud disk, under which the desired initial condition for such self-similar collapse can be set up. It is also found that the collapse can proceed even for equilibrium clouds that are linearly stable, an indication of the existence of metastable equilibria for gravitational collapse. The present analysis of self-similar spherical collapse rests critically on the assumption of the domination of small-scale magnetic fields over large-scale fields in the collapsing cloud. Whether such situations can indeed occur in nature is a subject that awaits further careful examination.