The unnamed woman, said to be in her 60s, was having dental implants when the drill head came loose from the surgeon's grip and fell into her mouth.
She was pulled into a sitting position, but it was too late to stop the part heading south, the 'Daily Mail' reported.
The woman was a patient at Vastmanland County Hospital in Vasteras, in central Sweden.
"She tried to spit it out, and was made to cough, but she'd already swallowed," the hospital's medical boss Per Weitz told 'The Local', an English language newspaper in Sweden.
The drill head is said to have been three centimetres long. When an X-ray was performed on the woman, it revealed the part had lodged itself in her right lung.
Doctors then immediately performed a bronchoscopy - an examination of the major air passages of the lungs - to remove it.
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"A pinky-sized tube was sent into her lung with a small camera and pliers to grab hold of the drill," said Weitz.
The patient was able to leave the hospital the day after her bronchoscopy, but it apparently took her a month to get over the ordeal.
The hospital has now introduced new procedures to try and avoid the event from happening again.
These include double-checking that the drill head is attached properly, and testing it in the air before using it on a patient.
But Weitz did acknowledge the new plan may not be fail-safe.
"Unfortunately, drills are going to be dropped every now and then," he added.