The 31-year-old fashion designer and the 77-year-old Beatles member bumped into each other Friday in the first-class section of their international flight.
RiRi documented them joking around on Instagram Stories, calling the occasion a "RihUnion."
"I'm about to put you on blast, Mr. McCartney," she laughed. "How are you on my flight?! Who is this peasant filming this legend?!"
"Who is this filming me?" joked McCartney. "Yeah, that's what I mean."
The unexpected duo last teamed up in 2015 on their single "FourFive Seconds" with Kanye West, which they performed at the 57th annual Grammy Awards and at the Desert Trip Weekend in 2016.
McCartney told DIY how "FourFiveSeconds" originated. “We ended up just talking a lot," he explained. “I played a few little things and one of them ended up as ‘FourFiveSeconds’ with Rihanna."
"It’s more a question of me feeling lucky that these people are interested [in working with me] and think that I can bring something to it. For me, I feel great. I like diversity," he added.