Maria Fernandez Martinez Jimene died of blood loss after her leg was ripped off during the horrific incident.
The 26 year-old was swimming off Melaque beach in the state of Jalisco on Saturday when the attack took place.
Local authorities said she had been helping her daughter to safety on a floating platform about 65ft off shore.
Videos on social media surfaced over the weekend, appearing to show rescue efforts and people shouting “she’s lost her leg”.
The civil protection service in Cihuatlán, the region the beach is in, said officers received a report of a person with difficulty getting out of the sea.
A statement read: “Upon arrival, a female is seen without vital signs and one of her legs severed, apparently caused by a shark attack.”
Local authorities issued warnings to locals and closed several beaches in the area. 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.
“We are working in collaboration with the appropriate authorities to evaluate the situation and take the necessary measures to guarantee security on our beaches.”
Ms Martinez Jimenez was a marine biology a student at University of Guadalajara. Her child was reportedly unharmed.
Friends and family took to social media to share their grief following her tragic death.
One friend wrote: “I want to express my condolences, love and support to the Martinez Arreguín family, for the sensitive passing of Maria Fernanda Martinez Jimenez.
“I accompany in your pain and sorrow to this great family that I appreciate as my own, especially at this moment to my great friend Angel Martinez. I am with you all. Ibaé, Rest In Peace.”
Shark attacks are rare in the region. Local government officials said that there had been no record of an incident on the beaches of Jalisco in 60 years.
They added that they are planning to install surveillance towers on the beaches and said the beaches will remain closed until Friday.
It comes after an American bride was killed by a shark while paddleboarding in Bahamas on Monday morning, after tying the knot on Sunday.