The movie star was trying to avoid people at the screening and was making his way back to his family after hiding out in the bathroom when he was accosted by the Oscar winner.
He recalls, "I was sneaking out and coming charging across a huge lobby was Sean Penn by himself and I hadn't met him yet, and I saw him and went, 'Oh no, he would have been so much better for this part.'
"I was looking for somewhere to hide, but there was nowhere to hide and he spotted me and came directly towards me, I thought to tell me that he would have been better for the part, and he came up to me and he said, 'Hey man, loved you in the movie. Let's go and get a drink.'
"(I was like), 'Ok, cool, let's get a drink,' so we walked into a bar and I left my family, everyone at the movie... It was Sean Penn... I'm thinking, 'Oh my God, I'm having a drink with Sean Penn.'"
But Ruffalo's nerves quickly got the best of him when he realised he'd have to order something manly to impress his new drinking buddy: "The bartender comes up and Sean says, 'What are you having?' and I said, 'Well... I guess I'll take a Maker's Mark double, neat,' and I said, 'What are you gonna have?' and he says, 'I'll have a white Russian (cocktail)', and so I changed my drink order to a white Russian, which is what I wanted."