Civil Protection workers and firefighters in the municipality of Cihuatlan, which includes Melaque Beach, said in a message after the incident: "Our officials were carrying out support activities during a swimming event in the bay when they received reports of a person who was having problems getting out of the sea.
"When they reached the area they discovered a woman who was lifeless with one of her legs amputated, apparently following a shark attack."
Cihuatlan’s municipal government said: ‘"Following the terrible incident off one of our beaches, our priority is guaranteeing the safety and wellbeing of all our citizens.
"That’s why we’ve decided on a precautionary measure of banning access to beaches until further notice."
The attack on Saturday morning is said to have occurred just 65 feet from the shoreline as a swimming race was taking place.
The dead woman is believed to be a former marine biology student at the University of Guadalajara.
In a Facebook tribute, university chiefs said they shared the pain of the victim’s friends and family, adding: "We express our condolences following this irreparable loss."
Well-wishers later left flowers for the victim at the spot where she died on the beach.