Gabriel Mongenot Santana Milhomem Santos, 25, a fan who had travelled from the country's centre-west region to see Swift, was stabbed to death on a Copacabana beach early on Monday, Rio's police said.
It was the second death of a Swift fan in four days after 23-year-old Ana Clara Benevides Machado fell ill during the singer's first show in the city on Friday, and died later that evening at a hospital.
Fans also reported fainting from extreme heat, being mugged or getting caught up in a police raid.
Rio's Municipal Health Department said Benevides, who, according to a friend, passed out during Swift's second song, Cruel Summer, experienced cardio-respiratory arrest, but the exact cause of her death is not yet known.
In a statement posted on Instagram, Swift said Benevides' death left her with a "shattered heart".
Before the show on Friday, fans lined up for hours outside the Nilton Santos Olympic Stadium where temperatures soared to 41C.
Taylor Swift was forced to postpone a Rio show due to the extreme temperatures in Rio.
Inside the stadium, concertgoers complained of unbearable heat and some said they had difficulty getting access to water.
"I didn't imagine that my dream could turn into a nightmare," said fan Kléssia Menezes, who told R7 TV that she became stuck with hundreds of other people on one of the ramps to a VIP area on Saturday as security officers blocked the entrance.
Once security let them through, she said, people started running and she fell on a hot metallic floor that burned her leg and back.
Ultimately, that night's show was postponed after tens of thousands of fans had spent hours lining up in the heat.
Swift announced on Instagram that it was necessary "due to the extreme temperatures in Rio".
The postponement was followed by chaos outside the stadium. Under a light rain, a mass of concertgoers left the area, which is close to one of Rio's working-class neighbourhoods, known as favelas.
Videos shared on social media showed groups of pickpockets robbing fans of their belongings, scenes not so unusual to Rio residents but far from the postcards many tourists have seen of the "cidade maravilhosa".
Many took refuge inside a Burger King, ducking for cover under tables and behind the counter in the kitchen area.
Heavily armed police raided the fast food restaurant's basement as loud sirens blared and those stuck outside the restaurant shouted.
Saturday's show was postponed to Monday night, but many who had travelled from other regions of Brazil and outside the country had already made plans to leave earlier.
"We're not going to be able to make it," said Hely Olivares, a 41 year-old Venezuelan who had travelled from Panama.
"A lot of people have wasted their journey."
