Ms Coffey, who has also served as health secretary and environment secretary, said her sister Clare raised the alarm after she began hallucinating and slurring her words - prompting her to seek treatment.
In an interview with the Sunday Times, Ms Coffey blamed the brain abscess on the stress of her role at the time as a junior environment minister.
She said: “I just overdid it and burned the candle at both ends.
“Michael Gove had come in as environment secretary and had really upped the pace and was really pushing on a variety of issues, and we were working very long hours trying to get stuff done and really trying to make a difference.
“I came close to dying, and I think looking back that if my sister hadn’t phoned St Thomas’s [hospital] and they hadn’t done that scan, I probably would have been dead in a matter of days.”
Ms Coffey described how Clare, who works in her parliamentary office, had “never known me the way I was” and phoned the hospital to raise concerns.
A scan was performed at St Thomas’ Hospital, near parliament, and the abscess was discovered.
The hospital then phoned her home and said “somebody needs to get here quickly”, Ms Coffey added. She said: “So my mum, who must have been in her eighties by then, came up and we did the flashing blues and twos down to King’s College hospital and I was operated on that night.”
Ms Coffey said: “I woke up the next morning, and the thing I was most distressed about was that I had lost my eyebrows. They had just gone. I think it was just the stress of it all.”
Ms Coffey resigned as a minister last month ahead of Rishi Sunak’s reshuffle and now tries to "live in the moment" after giving up the pressure of her role on the front bench.
Ms Coffey said: “I do value life more now than ever. I came close to dying, and I think looking back that if my sister hadn’t phoned St Thomas’ Hospital and they hadn’t done that scan, I probably would have been dead in a matter of days.”