The St. Louis Cardinals outfielder slammed into the bullpen wall as he reached over to take a spectacular catch in the second inning.
Ortiz was credited with a sacrifice fly that gave the Red Sox a 5-0 lead but Beltran paid a hefty price for his athleticism.
He did not return to the game in the next inning and team officials said he was taken to hospital for tests on his ribs.
Beltran's departure spoiled what had been a long-overdue first appearance in the World Series for the 36-year-old, playing his 16th season in Major League Baseball.
Beltran boasts the seventh-best postseason on-base percentage and slugging average in MLB history, but had never made it to the World Series.
Before this season, Beltran had been one win away from a World Series berth six times but his team lost them all.
Beltran struck out in his only at bat on Wednesday.