Officials said there were no other reports of casualties or damage.
The Athens Geodynamic Institute said the quake occurred around 70km south of the island in the Aegean sea, at a depth of about 13km.
Panagiotis Efstathiou of the National Health Operations Centre told reporters the 56-year-old woman was killed after she tripped and hit her head as she tried to leave her house in the village of Archangelos in a panic when the earthquake struck.
She was cradling her two-year old granddaughter in her arms at the time but the child was unharmed.
The early morning quake awoke people in Rhodes and sent hundreds out into the streets.
Police said there was no major reported damage to buildings, but that emergency services were on alert.
One hotel was evacuated as a precaution.
