Wednesday's friendly between England and Holland was cancelled, Saturday's Premier League fixture between Tottenham Hotspur and Everton has been called off, while the football league and Carling Cup have also been affected.
"[I'm] very saddened. When an England game or football game is called off, it's very sad," Terry told BBC Sport.
"But what we're seeing is devastating images of what's happening out there in the communities for families and businesses.
"All we urge for is calm on the streets and the safety of the public," he added.
Chelsea begin their Premier League campaign on Sunday away at Stoke City.