Shaw, who is averaging 19.5 points per game and leads the team in rebounds with 71, said before Wednesday's game that he'd likely miss at least two weeks. He had an X-ray taken earlier in the week.
St. Francis stayed close with Alemany (7-7, 1-0 in league) early into the fourth quarter, but the Golden Knights couldn't get past the athletic Warriors.
Both teams struggled mightily in the second quarter. Alemany made one basket and St. Francis made three.
"That was a typical early January game," said St. Francis Coach John Jordan, whose team lost its third consecutive contest. "Maybe because both schools are still on winter vacation.
"Both teams played well defensively. We tried to get a feel from where are points are going to come from with not having Braden. It's something we have to deal with. Injuries and eligibility can always be factors."
St. Francis turned to junior guard John Aranda, who paced the Golden Knights with a team-high 13 points. Aranda had eight first-half points.
Teammates Steve Vargas and Malik Speed each had nine points and three steals.
A three-pointer by Speed cut Alemany's lead to 38-36 with 5:08 remaining in the game.
However, Alemany closed out the game with an 11-5 run.
The Warriors, who stretched their winning streak to two after losing three consecutive games, received a game-high 16 points from senior shooting guard Britt Cook. Cook had a key steal in the final seconds of the third quarter and parlayed it into a basket to give the Warriors a 31-27 lead.
Jordan said the Golden Knights, who went winless in 12 league games last season, will need to regroup quickly without Shaw. St. Francis embarks on a three-game road trip, beginning at 7 p.m. Friday against Chaminade.