PayPal Holdings Inc. is withdrawing from the group of companies Facebook Inc. assembled to launch a global cryptocurrency-based payments network, dealing a blow to the social-media giant’s ambitions to transform financial services.

The San Jose-based payments company “made the decision to forgo further participation” in the Libra Association, the group backing the libra cryptocurrency, a spokesman said in an email. PayPal remains supportive of libra’s mission and will continue to discuss how to work together in the future,...