COVID-19’s impact on individuals, enterprises, and organizations is undeniable. Many markets, in particular, financial markets, have experienced considerable shock and suffered massive losses. Supply chain networks have encountered significant problems, especially in terms of financing. Supply chain finance (SCF), responsible for financing the supply chain components and improving supply chain performance, received a significant impact of COVID-19 consequences. Financial providers are the leading resource for supply chain finance. The banking sector is known as the main element of financing among financial providers. Any disruption in the banking system procedures can have a significant impact on the financing process. In this paper, we have tried to understand the essential effects of the COVID-19 pandemic on the banking sector. A hybrid approach consists of a novel and extended intuitionistic fuzzy best-worst method (IFBWM) to determine the critical factors’ weights, and a fuzzy inference system to get the performance index of the banking sector is utilized. The proposed method investigates the banking sector’s role in supply chain finance, specifies the principal risks of this sector in emergencies such as pandemics. The Turkish banking sector’s performance in three different periods is considered to demonstrate the validity and applicability of the proposed approach. The results depict that credit risk, loss of income, and liquidity were the most critical factors of the COVID-19 outbreak in the banking sector. Also, the Turkish banking sector’s performance has worsened with the spread and continuation of the COVID-19. Moreover, the cogency of the proposed method is verified through a brief comparative analysis.