Sveriges Television (SVT) reported that 71-year-old Birgitta Almeby died at the Karolinska Hospital in Stockholm late on Wednesday.
She was receiving treatment after having been flown home to Sweden for specialist medical care for her injuries.
Niclas Lindgren, director of the missionary wing of the Pentecostal church in Sweden, said it was hard to come to grips with Almeby's killing.
“Birgitta worked with social issues like education and health care. If she'd worked with political issues, it may have been understandable why she got murdered,” he told The Local.
“There was no indication that there was a threat to her life. It was very unexpected. As it is now, we don't know what the motive was or why she was killed.”
Lindgren added that it was "too early to say" whether the murder will affect the missionary's work in Pakistan.
Speaking with Christian newspaper Dagen, a representative from the Pentecostal church in Köping said Almeby's injuries had resulted in serious brain damage, leaving little hope that she would ever fully recover.
Almeby was attacked in Lahore, Pakistan's second largest city, on the eastern border with India last Monday.
"She was returning from her office and was attacked when she arrived in front of her home in the Model Town neighbourhood," Awais Malik, a senior police official told AFP.
She was working in Lahore for the US-founded Full Gospel Assemblies, which describes itself as a "church fellowship" with congregations all over the world.
The woman had lived in Pakistan for almost forty years.
Malik said on Monday that the culprits had not yet been identified.
The missionary wing of the Pentecostal church in Sweden still has one family in Pakistan, according to press officer Noomi Lind:
“But they are safe at the moment, as far as we can see. So they are going to stay for the time being,” she told The Local.
Lahore, a city of eight million, suffered a string of high-profile bombings blamed on Taliban and al-Qaeda-linked militants in 2010.
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In August 2011, US development worker Warren Weinstein was kidnapped after gunmen tricked their way into his Lahore home. Pakistani officials believe he is being held by al-Qaeda and Taliban extremists in Pakistan's lawless
In April, a British Muslim Red Cross worker was beheaded nearly four months after being kidnapped in the southwestern city of Quetta.