Coach Chan Gailey gave the injury updates at his weekly news conference Monday, confirming an earlier report by ESPN NFL Insider Adam Schefter.
An MRI exam completed on Jackson's right knee Monday revealed nothing conclusive, a source familiar with result had earlier told Schefter. It likely will be 7-10 days before a timeline is established for his return but a source estimated that the running back will miss at least a month.
Jackson told Bills fans via his Twitter page that he'll be back on the field as soon as possible.
He wrote: "Thanks for all the prayers all well wishes. I will get back on field ASAP! Keep Billieving in us, jus more work to do!!"
Nelson, meanwhile, tore the ACL in his right knee Sunday, a league source told Schefter. Before his injury, Nelson had two catches for 31 yards Sunday. He was the team's second-leading receiver in 2011, finishing with 61 receptions for 658 yards and five touchdowns.
Both players were injured in the Bills' 48-28 Week 1 blowout loss to the New York Jets.
Jackson, who went on injured reserve last November with a broken right leg, went down with 11:07 left in the first half Sunday when he ran for 7 yards and was hit hard by LaRon Landry. Jackson went down immediately and stayed down for a few moments while he was checked by trainers before walking on his own to the sideline.
C.J. Spiller replaced him and got the Bills on the scoreboard, zipping past a few missed tackles by Landry and Bart Scott and scooting into the end zone for a career-best 56-yard score. Spiller finished with a career-best 169 yards rushing.
Nelson was hurt early into the fourth quarter when he went down away from the play. After being helped off the field, he was spotted walking on the injured leg along the sideline.
Jackson finished 2011 with 934 yards and six touchdowns. He has rushed for at least 900 yards in each of the last three seasons, including 2009 when he had a career-best 1,062 rushing yards.
Both injuries are significant blows to the Bills, who entered the season with high expectations of their chances of becoming bona fide contenders.
Jackson was expected to provide Buffalo's running attack a considerable one-two punch along with Spiller. Now, Buffalo is suddenly thin at the running back position, with Tashard Choice serving as the lone backup.
The depth is no better at receiver as a result of Nelson's injury.
In opening the season with six receivers, including Brad Smith, who doubles as the team's Wildcat quarterback, the Bills were already thin and limping at the position to begin with.
Starter Stevie Johnson had four catches for 55 yards and a touchdown against the Jets despite being hampered by a groin injury that nagged him for much of the offseason. And there are concerns that Johnson will have to continue playing through the pain for the rest of this year.
Information from The Associated Press was used in this report.