IBM shares sank 13.2%, their biggest drop since October 18, 2000.
COBOL is a programming language widely used on IBM mainframes across banking, insurance and government systems.
"Modernizing a COBOL system once required armies of consultants spending years mapping workflows. Tools like Claude Code can automate the exploration and analysis phases that consume most of the effort in COBOL modernization," Anthropic said in a blog post on Monday.
"With AI, teams can modernize their COBOL codebase in quarters instead of years," it added.
Software stocks have been battered in recent months by market fears around the growing capabilities of AI tools, particularly following the launch of plug-ins from Anthropic's large language model Claude, seen as the startup's push to become an application layer.
Shares of cybersecurity companies including CrowdStrike CRWD.O and Datadog DDOG.O also slumped on Monday, as investors weighed the potential impact of Anthropic's new security tool on the industry.
(Reporting by Chris Thomas in Mexico City; Editing by Janane Venkatraman)

Ana Paula Assis, the general manager for IBM Latin America, poses during an interview in Bogota, Colombia, 28 November 2018 (issued 29 November 2018). Colombia will be the first country in Latin America to adopt the P-TECH educational model to train young people and grant them technical work titles in areas related to science, technology, engineering and mathematics (STEM). The plan was presented in Bogota by IBM together with two Colombian state entities. EPA-EFE/OSKAR BURGOS