Mathieu was hit during the third quarter of the Cardinals' 30-10 win over the St Louis Rams on Sunday before attempting to jog off the field only for his left leg to give way.
The rookie went for an MRI scan yesterday, where it was confirmed that he has torn both the ACL and LCL in his left knee and would require surgery.
"This will be a long one. But I won't attempt to say how long because it's [different with] individual guys now," Arians told reporters.
The Cardinals coach admitted that it is unlikely that Mathieu would be fit in time for the start of next season's training camp, but believes that the injury should not hamper his chances of being named as the defensive rookie of the year.
"I still think he should get rookie of the year defensively. The job he did in the three positions that he's played was outstanding," Arians added.
"I don't know if it'll hurt him to where somebody else will get it. There's some other deserving guys out there also. He meant a lot to us because of the flexibility in his positions. It'll take two guys to take his place."
The Cardinals are currently third in the NFC West and still have an outside chance of reaching the NFL playoffs with three games remaining.