Birgitta Almeby, a 70-year-old worker of the NGO Full Gospel Assemblies of Pakistan, was attacked near her residence in Model Town of Lahore on December 3.
FGA spokesman Liaquat Qaiser had described the incident as a "targeted attack".
Ali Usman, a doctor of Jinnah Hospital, said Almeby was flown home as the Swedish government believed she could be provided better treatment there.
"She is still unconscious as the bullets had damaged her lungs and jugular vein," Usman said.
The Swedish government sent an air ambulance with a special team of doctors to transport Almeby.
Other officials said Almeby was taken to Sweden as there were fears about her security.
Senior police officer Liaquat Malik told PTI that a Swedish policewoman had come to Lahore and inquired about the investigation into the attack.
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"We are investigating the matter and hopefully will soon get a clue about the attackers," Malik said.
Two unidentified men had visited Almeby's home a few days before the shooting and assaulted her private security guard.
Almeby has been living in Pakistan for over three decades and has been running several welfare programmes, including a midwifery course and technical courses.