According to Fox's Jay Glazer, Murray, Burton, Washington and running backs coach Joel Thomas were placed on the reserve/COVID-19 list after Kamara was placed on the list Friday.
Glazer noted that the Saints will move Ty Montgomery back to running back from wide receiver and call a running back up from the practice squad for Sunday's game.
On the season, Kamara has rushed for 932 yards and 16 touchdowns while catching 83 passes for 756 yards and five scores.
The bulk of the backfield load without Kamara in the lineup normally would go to Murray. As the main complement, he has rushed for 656 yards and four touchdowns. He has also caught 23 passes for 176 yards and a score.
Burton is a fullback, and Washington is a reserve running back who has just eight carries.
While Montgomery was primarily a wide receiver at Stanford, he has no shortage of experience at running back.
His most productive season at that position came with Green Bay in 2016, when he rushed 77 times for 457 yards and three touchdowns while reeling in 44 passes for 348 yards.
The only running back listed on the Saints practice squad is Tony Jones Jr., so he figures to get the call.
Jones played four seasons at Notre Dame, and his best statistical year was his senior campaign in 2019, when he rushed for 857 yards and six touchdowns on 144 carries while catching 15 passes for 104 yards and a score.
With few options at running back, the Saints may take to the air more often with quarterback Drew Brees. Head coach Sean Payton could also look to integrate backup quarterback Taysom Hill and his rushing ability more often.
The Saints have already clinched the NFC South and a playoff spot, so Sunday's game isn't of paramount importance, but they could still earn the No. 1 seed and a first-round bye with a win plus a Packers loss and Seattle Seahawks win.