The tight end is listed as questionable for tomorrow's game against the New Orleans Saints with the injury, which was sustained in the third quarter of the 49-9 defeat to the Cincinnati Bengals last Sunday.
Head coach Rex Ryan told reporters: "He was limited today. He was in a non-contact jersey. Again, the protocol for those concussion tests and all that, obviously he's going through that.
"I know he's still going through it. He probably wasn't cleared yet. I know he's still probably going through some of the testing."
Cumberland has 248 receiving yards and two touchdowns so far this season.