The magnetic properties of ZnCr2 O4 compound is studied both in the bulk and nanoparticle (prepared by ball milling method) forms. The bulk sample undergoes an antiferromagnetic ordering at = 13 K which concurrently occurs with a first order structural transition. The signature of this transition in magnetization data for the nanoparticle sample is found to be substantially weaker and the associated thermal hysteresis disappears completely. The nano-sample shows thermomagnetic irreversibility below along with hysteresis loop in the isothermal magnetization versus field data at low temperature. The hysteresis shifts from the origin on field-cooling thereby indicating the existence of exchange bias effect in the sample. Emergence of such anomalous features are found to be associated with the significant enhancement of surface disorder due to reduced particle size.