COVID-19 has induced many problems in various sectors of life for humanity around the world. After one year of pandemic, many studies have been carried out in exposing various technology innovations and applications to combat the coronavirus that has killed more people than most. The pandemic has accelerated the use of Big Data technology to mitigate the threats of COVID-19. This survey aims to explore the Big Data research for COVID-19. We collected and analyzed the relevant academic articles to identify how Big Data technology can cover the challenges faced in overcoming the pandemic. In determining the research areas addressed by the past studies, we highlight the technology contributions to five major areas of healthcare, social life, government policy, business and management, and the environment. We discuss how analytical techniques of machine learning, deep learning, statistics, and mathematics can solve pandemic issues. The Big Data research for COVID-19 used a wide variety of data sources available publicly or privately. At the end of the discussion, we present the data source used in the past studies encompassing government official data, institutional service data, IoT generated data, online media data, and open data. We hope that this survey will clarify the role of Big Data technology in enhancing the research for COVID-19.