The new couple had a lunch date on Saturday, June 26, at Rick's Drive In & Out in Los Angeles, Calif., PEOPLE reported.
The comedian and the 40-year-old were photographed smiling and laughing as they sat outside and chatted.
"They were having a great time during lunch, laughing and talking," a source told the outlet. "They were really enjoying each other's company."
The pair were first linked together last month, in the wake of Mulaney's split from his estranged wife Anna Marie Tendler.
The news that the comedian filed for divorce broke on May 10. Tendler was also reportedly in rehab at the same time, due to emotional reasons and alleged infidelity.
An OK! insider said that Tendler was "blindsided" after Mulaney pulled the plug on their six-year marriage. The insider also claimed that Munn was "ready to pounce," as "she and John had exchanged texts while he was in rehab, and things obviously turned romantic after he got out."
"People definitely have mixed feelings about his new relationship," the insider noted of Mulaney's friends, as he "he broke Anna's heart." The former flames tied the knot in 2014.
Mulaney and Munn first met several years ago at a wedding. "I was like, 'Oh, my gosh, do you and your fiancée [Tendler] want to go have dinner or something and go hang out?'" Munn told HuffPost Live in 2015.
However, Munn said afterwards that Mulaney never responded to her email, but she "might've got the wrong email — probably. That's what I tell myself," she joked.
The news that Mulaney was going to rehab broke in December. As previously reported by OK!, he entered a rehab facility in Pennsylvania for 60 days to seek treatment for alcohol and cocaine addition following a relapse.
Munn was one of the many stars who offered their well wishes at the time. "Sending SO MUCH love and support to John Mulaney. You got this," she tweeted.
"It was a relief to his wife and family that he checked in. It was John’s decision. Plain and simple, John had too much downtime. He had too much time in his own head," an insider had spilled to Us Weekly before the split. "John has always been engaged in his sobriety. The relapse got ugly, but it was his choice to go to rehab, which saved his life."
Since completing the rehab stint in February, Mulaney has been busy with his "From Scratch" stand-up shows.