Munn posted a collection of photos on Sunday including a shot alongside Mulaney holding their newborn, Méi June Mulaney. The couple welcomed their daughter earlier this month via a surrogate.
"Méi June Mulaney came into the world September 14, 2024, the year of the dragon," Munn wrote.
"I had so many profound emotions about not being able to carry my daughter," she added.
The actress was diagnosed with Luminal B breast cancer in both breasts in April 2023. Munn revealed in March that she underwent a double mastectomy among other surgeries in the months following her breast cancer diagnosis. She also opened up about undergoing a hysterectomy in the wake of her cancer treatment.
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"When I first met our gestational surrogate we spoke mother to mother. She showed me so much grace and understanding, I knew I had found a real-life angel," wrote Munn.
She continued to express gratitude for the gestational surrogate who carried Munn and Mulaney's child.
"Words cannot express my gratitude that she kept our baby safe for 9 months and made our dreams come true," she wrote.
"I am so proud of my little plum, my little dragon for making the journey to be with us. My heart has exploded," Munn continued.
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She ended the post with a note clarifying the pronunciation of her newborn. "Méi (pronounced may) means plum in Chinese ," she finished.
Mulaney also took to Instagram to celebrate the news writing, "We stole so much stuff from the hospital. I love my little girl so much."
Mulaney and Munn, who wed this year, also share a son, Malcolm, who they welcomed on Nov. 24, 2021.
In an interview with "Good Morning America" in May, Munn discussed fertility issues and the idea of pursuing surrogacy as a result of her health issues.
"John and I had a long talk about it. We realized that we weren't done growing our family," Munn said. "So right after the double mastectomy, I went through a round of egg retrieval and that's a scary process because I have a cancer that feeds off of hormones so I knew there was a risk."
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"And our doctor said, 'Look, we're gonna get one for you and then we're gonna call it,'" she continued. "And then our doctor called and he said, 'Hey, we got the results back. It's two healthy embryos.' And I, we, I mean, just started bawling, crying, both of us."