The present disclosure relates to a pre-5th-Generation (5G) or 5G communication system to be provided for supporting higher data rates beyond 4th-Generation (4G) communication system such as a Long Term Evolution (LTE).The present disclosure provides a method and system for enabling discontinuous reception (DRX) over an unlicensed band in cellular networks. In one embodiment, the method comprises of monitoring, by a user equipment (UE), an unlicensed channel at a pre-configured on period of a DRX cycle, wherein the UE wakes up during a DRX on period and sleeps during DRX off period, receiving an indication of extension of the DRX on period from an associated evolved node B (eNB) when the associated eNB is unable to acquire an unlicensed channel during a DRX on period of the licensed channel and continuously monitoring the unlicensed band for the extended DRX on period. The time period for extension of the DRX on period of the unlicensed channel is selected from a set of pre-specified extension values. The present disclosure further enables the UE to terminate monitoring of the DRX on period of the unlicensed channel upon receiving a stop monitoring indication from the associated eNB.