Parnaby suffered a torn hamstring during Saturday's 4-1 defeat at Crystal Palace and faces a lengthy spell on the sidelines.
Veteran Kieron Dyer replaced him on the day and could deputise at full-back while Stephen McManus offers further options at the back.
Manager Tony Mowbray has concerns elsewhere with Seb Hines (knee), Jonathan Woodgate and Scott McDonald (both calf) all doubtful for the clash.
McDonald faces a late assessment while Woodgate and Hines are not expected to travel to Turf Moor.
Long-term absentees Julio Arca (toe) and Justin Hoyte (hip) remain sidelined.
Boro have lost six of their last seven league matches but are still four points clear of seventh-placed Brighton as they look to strengthen their position in the top six.