Johnson was injured in the third quarter of the Cardinals' Week 1 loss to the Detroit Lions after a hit from Glover Quin.
After Johnson left the contest, fifth-year man Kerwynn Williams took over the lead running back duties.
Johnson was limited to 23 yards rushing on 11 carries, and had six receptions for 68 yards.
Already one of the Cardinals' biggest question marks heading into 2017, the offensive line also started a banged up Mike Iupati, who was limited in practices heading into Sunday.
If Johnson were to be placed on the IR list, it would mean he would miss at least eight weeks of action before he would be eligible to return to the active roster.
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Re-signing Chris Johnson, who was cut on September 2, could be an option, Arians said.
He was hoping to chase history again in 2017, after finishing last season 121 yards from becoming just the third National Football League player in history to gain 1000 rushing and receiving yards. Veldheer was moved to right tackle in the offseason to make way for Humphries. X-rays after the game came back negative and suggested that the wrist was only sprained.
"I have all the confidence (in other backs)".
Arians said Palmer placed "super pressure on himself to be flawless instead of just play".
In a radio interview after his press conference, Arians explained a bit more: "He wants to find a way to play".
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