Justice Against Malicious Algorithms Act of 2021 This bill limits federal liability protection that applies to a provider of an interactive computer service (e.g., a social media company) for claims related to content provided by a third party if the provider makes personalized recommendations of online content that cause physical or emotional injury. Specifically, the liability protection (sometimes referred to as Section 230 protection) shall not apply to a service provider that has more than 5 million monthly visitors for more than 3 of the preceding 12 months, uses an algorithm or similar computational process to make personalized recommendations based on information specific to an individual, and knowingly or recklessly makes a personalized recommendation that materially contributes to a physical or severe emotional injury to a person. However, the liability protection shall continue to apply to (1) recommendations made directly in response to a user's search; and (2) service providers of web hosting, domain registration, data storage, and related services that are used by another service provider in the management, control, or operation of that provider's services.