We demonstrate the existence of Q-balls in nonminimally coupled inflation models with a complex inflaton in the Palatini formulation of gravity. We show that there exist Q-ball solutions which are compatible with inflation and we derive a window in the inflaton mass squared for which this is the case. In particular, we confirm the existence of Q-ball solutions with φ∼1017-1018 GeV, consistent with the range of field values following the end of slow-roll Palatini inflation. We study the Q-balls and their properties both numerically and in an analytical approximation. The existence of such Q-balls suggests that the complex inflaton condensate can fragment into Q-balls, and that there may be an analogous process for the case of a real inflaton with fragmentation to neutral oscillons. We discuss the possible postinflationary cosmology following the formation of Q-balls, including an early Q-ball matter domination (eMD) period and the effects of this on the reheating dynamics of the model, gravitational wave signatures which may be detectable in future experiments, and the possibility that Q-balls could lead to the formation of primordial black holes (PBHs). In particular, we show that Palatini Q-balls with field strengths typical of inflaton condensate fragmentation can directly form black holes with masses around 500 kg or more when the self-coupling is λ=0.1, resulting in very low (less than 100 GeV) reheating temperatures from black hole decay, with smaller black hole masses and larger reheating temperatures possible for smaller values of λ. Q-ball dark matter from nonminimally coupled Palatini inflation may also be a direction for future work.