"She is now out of surgery," a rep for Kathy Griffin tells PEOPLE, giving a positive update just hours after the comedian revealed her stage 1 lung cancer diagnosis

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Kathy Griffin is recovering from surgery after revealing her stage 1 lung cancer diagnosis.

The two-time Emmy Award winner, 60, revealed Monday morning that she was having part of her left lung removed. "She is now out of surgery and everything went well, per her doctor," a rep for Griffin tells PEOPLE.

Griffin had previously taken to social media to share a statement about her diagnosis and the road to recovery. "Yes, I have lung cancer even though I've never smoked!" Griffin wrote.

"The doctors are very optimistic as it is stage one and contained to my left lung," she continued. "Hopefully no chemo or radiation after this and I should have normal function with my breathing. I should be up and running as usual in a month or less."

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Griffin assured her followers that she will be "just fine" and urged them to stay current with their medical checkups, in addition to getting vaccinated against COVID-19, which could have made her diagnosis "even more serious."

"It's been a helluva 4 years, trying to get back to work, making you guys laugh and entertaining you, but I'm gonna be just fine," she concluded. "Of course I am fully vaccinated for Covid. The consequences for being unvaccinated would have been even more serious. Please stay up to date on your medical check ups. It'll save your life. XXOO, KG"

Last March, she faced a health scare when she experienced COVID-19-like symptoms amid the early days of the pandemic. At one point, she was admitted to an isolation ward room after experiencing "unbearably painful" symptoms, including nausea, diarrhea, chills and a sore throat.

The Suddenly Susan actress will shed more light on her cancer diagnosis in an interview with co-anchor Juju Chang airing Monday night on ABC News' Nightline (12:35 a.m. ET on ABC). In a clip from the sit-down, she says she is "still a little bit in shock" after finding out the news a few weeks ago.

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Courtesy Yashar Ali

"Really just days ago — like, I think two weeks ago — I was diagnosed with cancer," Griffin said in the clip. "As a friend of mine had said, 'How many kicks in the nuts can you take?' My nuts are pretty strong, but it's a challenge. I was definitely in shock. I'm still a little bit in shock — not denial, but once a day I'll just turn to like, nobody next to me and go, 'Can you believe this s---? Is this a bitch or what?'"

According to ABC, she will also discuss her mental health journey, her addiction to pills, a suicide attempt, her newfound sobriety and more.

Griffin has experienced a few losses to cancer in recent years, after her older brother Gary died at age 63 in 2014, following a stage 4 esophageal cancer diagnosis. Her sister Joyce died at age 65 in 2017, after undergoing chemotherapy. Griffin previously shaved her head a few months earlier, in solidarity with Joyce.

The comedian's mom Maggie died in March 2020. The year prior, in January 2019, Griffin had revealed that her mother had been diagnosed with dementia.