The move comes as part of a week of action by European anti-racism body Football Against Racism in Europe (FARE).
A Uefa spokesman told reporters: "The captains will be asked to wear a 'Unite Against Racism' branded armband."
Terry accepted in October a four-match ban and £220,000 fine from the FA for racially abusing QPR defender Anton Ferdinand last year.
However, the former England skipper is still eligible to play for his club in European matches as the ban only applies domestically.
The FARE campaign will be promoted at 40 matches across the Champions League and Europa League between October 16 and 31.
Uefa will be hoping for a more united response than was seen from the domestic Kick it Out campaign across England on Saturday and Sunday, as 32 players – including Rio Ferdinand and Jason Roberts – refused to wear a T-shirt supporting the initiative.