"Last night, I was up all night praying for my sister, Dolly," she wrote. "Many of you know she hasn't been feeling her best lately. I truly believe in the power of prayer, and I have been led to ask all of the world that loves her to be prayer warriors and pray with me."
She ended her plea on a more upbeat note: "She's strong, she's loved, and with all the prayers being lifted for her, I know in my heart she's going to be just fine. Godspeed, my sissy Dolly. We all love you!"
Freida later said: "I want to clear something up. I didn't mean to scare anyone or make it sound so serious when asking for prayers for Dolly. She's been a little under the weather, and I simply asked for prayers because I believe so strongly in the power of prayer. It was nothing more than a little sister asking for prayers for her big sister. Thank you all for lifting her up. Your love truly makes a difference."
* Dolly Parton's cabin with guitar-shaped toilet going for a song
The singer set the record straight herself in the Instagram video, saying: "I wanted to put everybody's mind at ease, those of you that seem to be real concerned, which I appreciate. And I appreciate your prayers, because I'm a person of faith. I can always use the prayers for anything and everything. But I want you to know that I'm OK."
She explained that in the wake of her husband Carl Dean's death this year, "I didn't take care of myself, so I let a lot of things go that I should have been taking care of."
Parton said she has had to cancel engagements to be closer to her Nashville hospital for "a few treatments here and there".
She also cracked a joke about an AI photo circulated online showing Reba McEntire, a fellow country singer, at Parton's deathbed.
"Ooh lordy," she said. "We both looked like we need to be buried! If I was really dying I don't think Reba would be the one at my deathbed."
She concluded: "I'm not ready to die yet, I don't think God is through with me and I ain't done workin'. So I love you for caring, and keep praying for me."
* Dolly Parton says she doesn't want to be brought back as a hologram
Parton's English manager Olly Rowland was quoted in The Mirror confirming that the worries were overblown. He said: "It's just the kidney stones and the procedure she needs to resolve those.
"It looks like her sister posted and it got quite a bit blown out of proportion, weirdly."
Last week Parton, whose hits include the 1973 single Jolene, postponed her Las Vegas residency and revealed she was due to undergo several medical procedures. She had been due to perform six nights of sold-out shows in December at the Colosseum at Caesars Palace, but said her health meant she would not "be able to rehearse and put together the show that you want to see".
She reassured her millions of followers she was not ending her career just yet and that the shows had been rescheduled for next September. The Vegas residency would have been her first in more than 30 years.
* Dolly Parton at 79: 'I go to bed with my make-up on'
Parton became a country music star in the 1970s and has sold more than 100 million records in a career spanning more than five decades. Her other hits include Coat of Many Colors, 9 to 5 and I Will Always Love You, which was covered by Whitney Houston for the 1992 film The Bodyguard. Parton has won ten Grammy awards and been nominated 55 times.
Dean, her husband of nearly 60 years, died in March this year at the age of 82. "Carl and I spent many wonderful years together," Parton wrote in a statement posted on social media. "Words can't do justice to the love we shared for over 60 years. Thank you for your prayers and sympathy."