The 55-year-old, from Southport, was on the back of a Vespa Piaggio when its driver, a 51-year-old man also from Southport, lost control because of the malfunction, a spokeswoman for Lancashire Police said.
She was taken to Royal Preston Hospital with life-threatening head and chest injuries. Her riding partner broke his shoulder but was not as badly hurt, she added.
Officers closed the Prom close to Norbreck Castle in North Shore – where the crash happened – at around 2.25pm yesterday.
It remained shut for almost three hours while accident investigation work was carried out.
Police are appealed for witnesses to come forward. Call 101 quoting log reference number 854 of September 18.