Jackson, ruled out for the game on Friday, injured his right thigh in the Rams' 34-14 win over Dallas on Oct. 19. He missed the next game at New England and had just 17 yards on seven carries in a 34-13 loss to Arizona last weekend.
Jackson told the NFL Network prior to Sunday's game he wanted to work out on Saturday and believed if he would have had one more day of rest, he could have played.
"We decided that another week's rest was best for the rest of season, and I understand that," Jackson said.
Darby has two carries for 9 yards in his NFL career. Signed off Atlanta's practice squad Oct. 15, he was a seventh-round draft choice last year by Tampa Bay and played in one game for the Buccaneers.
Samkon Gado, signed by the Rams on Tuesday, will be Darby's backup. Travis Minor is still dealing with a concussion and will not play.
For the Jets, leading tackler David Harris was inactive, as expected, after reportedly having surgery earlier this week on his injured groin. The linebacker is expected to miss at least two to three weeks after being hurt in the second quarter of New York's 28-24 victory over Kansas City on Oct. 26.
Safety Eric Smith (head) and tight end Bubba Franks (hip) were also previously ruled out for the game.
The Associated Press contributed to this report