Choreographed celebrations by two or more players aren't permitted, league spokesman Corry Rush said.
No flags were thrown at the time in the game.
Brown, right tackle Vernon Carey and right guard Ikechuku Ndukwe gathered in the end zone after Brown took a direct shotgun snap and ran 5 yards for what turned out to be the deciding touchdown.
The three then did a dance called the "Cupid Shuffle."
Brown told the South Florida Sun-Sentinel that he and the starting line had practiced their moves during last Friday's walk-through, and said left tackle Jake Long dropped out of the choreographed routine at the last minute because he didn't want to be fined.
"I was a little surprised about the amount more so than getting fined," Brown said. "Obviously we were out having fun and we were enjoying the game ... But at the same time, I guess rules are rules."
Brown and Carey have multimillion dollar contracts, but Ndukwe makes the league minimum for players with two credited NFL seasons: $445,000.
Ndukwe was signed last year off the Baltimore Ravens' practice squad and survived the final cuts in Dolphins training camp as a backup.
Ndukwe was asked how he'll handle future celebrations.
"No dancing for me," he said. "I'm running straight for the sideline."
Tim Graham covers the AFC East for ESPN.com. Information from The Associated Press was used in this report.