The concept of corporate sustainability suggests that firms need to maintain sustainability principles and practices by addressing stakeholders' economic, ecological, and social concerns. Social media has become a knowledge depository where managers can evaluate stakeholders' concerns about the firm's sustainability-related issues. This study proposes a computational approach that utilizes natural language processing techniques to detect sustainability-related communities within online web forums. The validity of the detected communities was assessed based on their impacts on relevant firms' market performance when the firms' social responsibility was challenged. Experiments on three datasets showed that our system is effective in detecting sustainability-related communities. Also, a strong correlation was found between the activities of the identified sustainability-related communities and the firms' market performance during events that challenged the firms' social responsibilities. Our research contributes to the practice of managing corporate sustainability by facilitating managers in evaluating sustainability-related concerns of stakeholders and making effective managerial responses.