The former England defender left the pitch in their 1-0 defeat to Hull City last weekend after complaining of concussion.
It was expected that he would return for Saturday's encounter, but Mowbray has claimed that the 33-year-old will be assessed this week.
Mowbray told the club's official website: "Jonathan had concussion and was being sick at half time on Saturday.
"He has been assessed by the doctors over the last few days, which is standard procedure with this type of injury. We will keep an eye on him and assess the position later in the week."
Middlesbrough currently sit ninth in the Championship table.