SNP MP Amy Callaghan had to undergo emergency neurosurgery after collapsing at home with a brain haemorrhage.
Ms Callaghan, who represents East Dunbartonshire, was found by her partner last Wednesday.
The 28-year-old is now recovering in hospital following an operation.
In a statement posted on Twitter, Ms Callaghan’s office said: “Thanks to the immense skill and response of the medical team involved in her care, Amy was able to successfully pull through the operation and it now stable in hospital.
“She wishes to put on record her enormous love and gratitude to all involved in her care – the first response and ambulance crew, accident and emergency staff, the neurological surgeons and the wonderful nursing team – who have all played a role in, undoubtedly, saving her life.”
“As she always has done, she will continue to fight. She is determined to overcome what barriers, if any, may now arise as a result of this incident.”
First Minister Nicola Sturgeon wished Ms Callaghan a quick recovery and sent her best wishes to the MP and her family.
She was joined by Prime Minister Boris Johnson who also sent the MP a message of support.
Speaking in the House of Commons, SNP housing spokesman David Linden described Ms Callaghan as a close friend.
He told MPs: “All of us in the SNP family and I’m sure in this wider house want to see Amy get back to full health.
“Amy is not just a colleague of mine here she is one of my closest friends here and I look forward to her coming back to resume her duties and be in her rightful place.”
Ms Callaghan was elected to the House of Commons in December after ousting the then Liberal Democrat leader Jo Swinson from her East Dunbartonshire seat.
The statement issued by her office said: “She has made great progress thus far but is under no illusion of the seriousness of her condition and the rehabilitation that will follow.
“She wants to make clear that her constituency work will continue: her office is still open for all those who require help and support.”
Ms Callaghan will need a “period of required rest and recovery”, it continued, but stated it was the “the privilege of her life” to have been elected in December.
“There is absolutely no doubt that Amy will come back stronger, fitter and more determined than ever to continue in that role and serve, to the best of her ability, the people of her constituency.”
SNP Westminster leader Ian Blackford MP said: “My thoughts and best wishes are with Amy and her family at this incredibly difficult time.
“I wish Amy a full and speedy recovery from everyone in the SNP, and would ask that people please respect her family’s privacy now and in the weeks to come.”