Passengers reported having to wait as medics went on to the flight to examine the stricken crew member, who was later taken from the aircraft to a waiting ambulance.
A Virgin Australia spokeswoman said the incident resulted in the aircraft not heading for Auckland as scheduled.
The passengers were put up various hotels and inns around the island, including the KiiKii Inn, the Edgewater Resort and Club Rarotonga.
CI News understands they left Rarotonga on Monday night.
It is the second incident to befall Virgin Australia in the past week. On Saturday a flight to Auckland returned two hours into its journey after a light came on in a cockpit instrument panel. As a safety precaution the aircraft returned to Rarotonga.
While most passengers found accommodation, some 18 did not. They spent the night outside the airport under an awning.
It is understood the Virgin Australia team on the ground liaised with local hotels, but were unable to secure accommodation for all passengers.
The spokeswoman said: “Virgin Australia flight VA90 landed safely in Raratonga at 2am on Saturday May 27 without incident.
“The safety of our guests, crew and aircraft was never in question.
“Engineers were required to replace a part and guests were moved to a new flight.
“We apologise for any inconvenience caused to guests by this disruption to their service.”
A local official said: “Normally, it is the airline’s, or their local representatives’, responsibility to assist stranded passengers.”