The stars, who split in early 2009 after a headline-grabbing fight, have sparked speculation of a reconciliation in recent months after being photographed together on a number of occasions.
Girls creator Dunham reveals she used to be a huge fan of the Umbrella hitmaker's music - but has been turned off the singer by her controversial behaviour and rumoured reunion with Brown.
In an interview with Alec Baldwin on his podcast, Dunham also calls on Rihanna to be a better role model for her young fans.
She says, "It's an amazing thing and it's like, it's a platform that you have to take seriously. Which is why sometimes, it's like, I used to be really into Rihanna, that pop star, and then it's like again, I don't want to ever throw stones from my glass house, but I follow her on Instagram and I just think about how many little girls beyond what I could even comprehend are obsessed with Rihanna.
"Like you know, she left Barbados, she's had this amazing career, she's won a Grammy... She's talented. And then she gets back together with Chris Brown and posts a million pictures of them smoking marijuana together on a bed. And it cracks my heart in half in a way that makes me feel like I'm 95 years old."
It's not the first time Dunham has commented on the controversial couple - last February (12), she wrote on her Twitter.com page, "Rihanna and Chris Brown's new duets make me want to go hide under Gloria Steinem's bed for 72 hours."