Earlier this week Terry accepted a four-match ban for using racist language towards Anton Ferdinand in a Premier League match at Queens Park Rangers.
Speaking to talkSPORT this morning, Buck revealed that Terry would not be suspended any further and keep the armband.
However, chief executive Ron Gourlay did say that the former England international had incurred a "very heavy fine".
Blues manager Roberto Di Matteo had yesterday refused to say whether the 31-year-old would remain skipper.
Terry begins his four-match stint on the sidelines when the Blues head to London rivals Tottenham Hotspur this afternoon.