Routing is critical in the Internet of Things (IoT) environment, which encompasses deployment of restrained devices like sensors and RFIDs in a large-scale. In the IoT environment, these restrained devices together form Low Power and Lossy Networks. The routing protocol assimilated for LLNs is Routing Protocol for Low power and Lossy Networks. The Root node solely manages the arrangement and maintenance of nodes present in the DODAG, via control messages, to disseminate the information of the network. Multiple nodes of the LLN in the DODAG are connected to the root node. Therefore, any node wants to join the DODAG must have connectivity with the root node. Adversary node isolates a group of IoT network nodes from the root node due to the vulnerability of the flow sequence of the control messages. In the Network Isolation Attack (NIA) specifically, an adversary node forms its own network without the knowledge of root node and victim nodes are unaware that they are not connected to the root node. This threat creates separate topology, packet loss etc in the network. In this paper, we propose a mitigation technique against the NIA in DODAG of 6LoWPAN network. The effect of the threat and mitigation technique is analyzed through simulation using Cooja simulator. The performance is analyzed in terms of metrics i.e, no. of devices isolated from the sink device and average Packet Delivery Ratio. The proposed mitigation technique performs better than RPL against NIA in DODAG.