The injury has taken the joy our of the win for Red coach Eddie Jones.
"He's (Brown) played just three games of Super 14 - against the Hurricanes, Highlanders and Hurricanes again - and he's always done the job for us," Jones said.
"His injury means he'll be out for a minimum of two weeks and hopefully less than four. We'll be disappointed to lose him."
Although Brown's injury put a dampener on the victory, Jones believes that the loss will pave the way for youngster Charlie Fetoai to have more game time after the 20-year-old replaced Brown after the injury.
"This opens up an opportunity for Charlie and for Lloyd Johansson - who becomes eligible for selection again this week - to make the starting side for Saturday's match against the Crusaders," Jones said.
Johansson and flyhalf Quade Cooper will become available for selection by Jones after the pair were disciplined for arriving at training late prior to the opening match.
After the upset victory over the Hurricanes, Jones was quick to praise man-of-the-match Berrick Barnes who used his kicking game well during the match.
"I was pleased with him," Jones said. "He played with nice composure, directed us around the field and generally kept the ball in front of us.
"It was a pretty good effort first-up."
The Reds face 2006 Super 14 champions the Crusaders in Christchurch next Saturday in round two action.