Jackson also said his injury typically keeps players out four weeks.
The 33-year-old suffered the injury in the first quarter of Buffalo's 17-16 win over the Minnesota Vikings, having to be helped off the field and later carted off after a low hit. He had three rushes for 12 yards and three catches for 16 yards before his departure.
Dixon, in his first year with the Bills after four years with the San Francisco 49ers, has 27 carries for 137 yards this season. Brown, also in his first year with the team after two seasons with the Philadelphia Eagles, hasn't yet been active for a game this season.
Jackson has 239 rushing yards, 261 receiving yards and two total touchdowns this season. In the offseason, Jackson signed a one-year contract extension that keeps the eighth-year pro with the Bills through the 2015 season.
The Bills are 4-3 this season after their win over the Vikings and are in second place in the AFC East. They play at the New York Jets this Sunday and then have a bye, which means Jackson could miss just three games if he is out four weeks.
- Ben Estes