"健康无疫证明书" can be translated as "Health Certificate of Freedom from Infectious Diseases" or more concisely as "Health and Epidemic-Free Certificate".
"Health Certificate of Freedom from Infectious Diseases" is a more literal and detailed translation, clearly indicating that the certificate verifies the holder's health status regarding infectious diseases.
"Health and Epidemic-Free Certificate" is a slightly more streamlined version that still conveys the essential meaning, emphasizing both health and the absence of epidemics.
Both translations are acceptable, and the choice between them may depend on the specific context or the preference of the institution issuing the certificate.