The 32-year-old midfielder had been listed as "questionable" for what would have been his second MLS match in four nights, but did not play to the disappointment of a sellout crowd of 35,402.
"It just didn't feel right," his coach Frank Yallop told reporters after the 1-0 New England victory. "He didn't want to risk it, so we decided not to."
After missing last Sunday's game at Toronto FC, Beckham made his MLS debut on Thursday at D.C. United, playing the final 18 minutes in a 1-0 loss before a capacity crowd of 46,686.
Yallop did not know if the former England captain would play at New York on Saturday.
"Hopefully, by Tuesday morning he'll feel a lot better," Yallop said.
Beckham has hinted he might not be able to play in games on artificial surfaces until the ankle is completely healed.
At halftime some fans, unaware that Beckham was not on the team sheet, still thought they would see him and a chant of "We Want Beckham" was heard in the 59th minute.
"David wants to be on the field," Yallop said. "I think he feels very bad. It's a disappointment, but it's a reality. I do feel for the fans because they're excited to see him play and so are we as a team."
The Galaxy's record is just 3-7-5 this season.
Beckham appeared 15 minutes before the game, signing autographs for members of a record crowd that was the Revolution's largest for an MLS regular-season game, around 21,000 above average.
"The impact (on the league) has been phenomenal," said New England coach Steve Nicol. "It's great for everybody."
Asked if he noticed a difference in the crowd, Nicol quipped, "Just a wee bit, yeah," and added, "The crowds we have are very enthusiastic, there's a good atmosphere here anyway. Obviously, with more people, it's even louder."