The former England international damaged a thigh muscle in Saturday's 1-0 home defeat by Brighton and did not reappear for the second half.
Woodgate is being assessed but must be considered a doubt for Saturday's Sky Bet Championship trip to Millwall.
The 33-year-old, whose career as been punctuated by fitness problems, has been a key figure during Karanka's reign to date, and an extended lay-off would represent a blow with the Teessiders currently sitting just three points clear of the drop zone.
The Spaniard at least has options with youngster Ben Gibson, who took over from Woodgate at the weekend, Australia international Rhys Williams and Seb Hines ready-made replacements should he miss out.
Boro face four important league games inside 12 days over the festive period, with Burnley and Reading visiting the Riverside Stadium between the trip to Millwall and a New Year's Day fixture at Bolton.
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