1743, borrowed (during an outbreak of the disease in Europe), from Italian influenza "influenza, epidemic," originally "visitation, influence (of the stars)," from Medieval Latin influentia in the astrological sense (see influence).
AN Article from Rome informs us that a Sort of Plague has broke out there, which destroys Abundance of their People, and they call it the Influenza. ["The Gentleman's Magazine," April 1743]
Used in Italian for diseases at least since 1504 (as in influenza di febbre scarlattina "scarlet fever") on notion of astral, occult, or atmospheric influence. The 1743 outbreak began in Italy. Often applied since mid-19c. to severe colds.