McKelvie took leave from her role as the alcohol and drugs policy minister last August to seek treatment for secondary breast cancer.
Her death was announced by her long-term partner, Keith Brown, depute leader of the SNP, in an emotional statement.
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McKelvie was first elected as a list MSP in 2007 before winning the Hamilton, Larkhall and Stonehouse constituency in 2011. She had announced her intention to retire from Holyrood at the next election.
Brown said: "Christina's sons, Lewis and Jack, and I are heartbroken to announce the death of Christina at Glasgow Royal Infirmary.
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"She loved her job, and she loved her party and was always a champion for the people of Scotland and an advocate for social justice and for Scotland to be an independent nation in Europe.
"To us, she was our beloved mum, partner and gran to Maeve and Leo. She was always hard-working and ...