"Shame on you. Throw the whole app-oligy away," she said in a statement posted Thursday.
Fans immediately cried foul after the game -- titled "Would You Rather!" and created by a developer called Daniel Lulic -- popped up on its app earlier this week.
Rihanna's relationship with ex-boyfriend Brown, 28, publicly ended after the two were involved in a February 2009 domestic violence incident.
In response, Snapchat pulled the game from its platform and subsequently blocked the advertiser, citing that the mobile video game ad didn't meet its advertising policies.
In a statement to ABC News on Thursday, a spokesperson for Snap Inc. said: "This advertisement is disgusting and never should have appeared on our service. We are so sorry we made the terrible mistake of allowing it through our review process. We are investigating how that happened so that we can make sure it never happens again."
Previously, Snap Inc. said in a statement released Monday that the "ad was reviewed and approved in error, as it violates our advertising guidelines. We immediately removed the ad last weekend, once we became aware. We are sorry that this happened."
Rihanna, 30, dismissed Snapchat's first apology in a statement posted to Instagram Thursday.
"Now Snapchat I know you already know you ain't my fav app out there! But I'm just trying to figure out what the point was with this mess!" she began. "I'd love to call it ignorance, but I know you ain't that dumb!"
The singer added that she was perplexed that the app would "intentionally bring shame to DV [domestic violence] victims" and make light of it.
"This isn't about my personal feelings, cause I don't have much of them...but all the women, children and men that have been victims of DV in the past and especially the ones who haven't made it out yet...you let us down," she wrote.
The former first daughter wrote on Twitter on Monday, "Just awful. Awful that anyone thinks this is funny. Awful that anyone thinks this is appropriate. Awful that any company would approve this."