In this paper, we propose a mobile blockchain (MB) based mining-as-a-service (MaaS) scheme, MB-MaaS for resource-constrained industrial internet-of-things (IIoT) environments. The scheme addresses the research gaps of fixed static allocation for miners to perform computationally intensive mining tasks through a multi-hop computational offloading (CO) scheme and addresses an auction mechanism for a fair bidding process among the miner nodes. The scheme operates in three phases. In the first phase, a multi-hop CO scheme with a fair incentive policy is formulated for miners. The CO schemes offer guaranteed offloading services to mobile devices from far-edge systems through a chain of neighbor nodes. Then, in the second phase, MaaS is proposed to leverage expensive mining tasks through 5G-enabled pico/femtocells. Integration of 5G allows massive end-to-end device and service connectivity. As IIoT ecosystems have limited memory and compute requirements, MaaS assures that the proposed consensus has a responsive validation and mining time. To make the data exchange in the consensus process lightweight, and allow a large number of sensors to share the data in a lightweight manner, an effective consensus mechanism Lightweight Proof-of-Proximity (LPoP), is proposed that forms group validations instead of single block validation. The data is exchanged through javascript object notation (JSON) format, maintaining a steady transaction rate. MB-MaaS is compared against the existing scheme for parameters bid thresholds and request servicing times, and mining and consensus formation. For example, the request serving time at 12 requests is improved by 56.78%, and a significant improvement of 26.47% is observed for processed blocks; parsing time on average is improved by 7.89%. The comparative analysis suggests that the scheme is more efficient than other competing approaches.