The mobility restrictions related to COVID-19 pandemic have resulted in the biggest disruption to individual mobilities in modern times. The crisis is clearly spatial in nature, and examining the geographical aspect is important in understanding the broad implications of the pandemic. The avalanche of mobile Big Data makes it possible to study the spatial effects of the crisis with spatiotemporal detail at the national and global scales. However, the current crisis also highlights serious limitations in the readiness to take the advantage of mobile Big Data for social good, both within and beyond the interests of health sector. We propose two strategical pathways for the future use of mobile Big Data for societal impact assessment, addressing access to both raw mobile Big Data as well as aggregated data products. Both pathways require careful considerations of privacy issues, harmonized and transparent methodologies, and attention to the representativeness, reliability and continuity of data. The goal is to be better prepared to use mobile Big Data in future crises.