SAN FRANCISCO — Alibaba.com Inc. has been hit with a class action lawsuit claiming that its network of e-commerce websites is home to rampant copyright infringement of visual artwork.

The lawsuit brought on behalf of professional Indiana artist Michel Keck seeks to certify a class of copyright holders who have seen their work copied and sold on Alibaba’s network of websites. The 81-page complaint, filed Monday in U.S. District Court for the Northern District of California, spins a Kafkaesque tale about Keck’s attempts to get dozens of China-based sellers to stop selling knock-offs and copies of her work—primarily modern abstract canvas prints that feature dog portraits and religious themes.