The 31-year-old came off an hour into Wednesday's Champions League quarter-final second leg clash against Benfica having initially suffered the injury in the first-leg victory in Lisbon.
Despite playing in Saturday's Premier League win over Aston Villa, Terry admitted he was gasping for air after Wednesday night's 2-1 win at Stamford Bridge.
John Terry. Photo:AFP
"I couldn't breathe and my chest was closing up," said Terry.
"I was having a difficult time out there, especially in the first half. Hopefully, I'll be okay.
"I don't know how long I'll be out. I will have a scan in the morning (Thursday) and we will see where we go from there. It's just horrible.
"When you get one in the ribs, you can't do anything about it, you can't treat it, you just have let it heal, but I can get through games definitely.
"I thought it was okay but, later in the second half, it just seemed to be getting worse and I was struggling to breathe to be honest.
"It was difficult. I have never felt anything like that before."
Chelsea struggled badly during Terry's absence with a knee injury earlier this year and it would be a blow if the captain were not available for their semi-final clash with champions Barcelona.
"It's a very good achievement to reach our sixth semi-final in nine years, but we want to go through to the end," said Terry.
"Clearly, that's going to be tough against Barcelona, but we're playing well.
"I am not sure anyone will fancy playing us at the moment because we are a very good side, especially in this competition. Barcelona are a very good team, but home and away we're a very solid side as well.
"We have shown that away against a very good Benfica side and proved on big nights at Stamford Bridge that we can really upset teams as well.
"We're confident. It is important we keep this momentum because we're going well in the league. That is the key for us."
Gary Cahill, who signed from Bolton in January, came on for Terry on Wednesday night and is confident of stepping in against Barca if necessary.
"I am ready to face them if selected. It is exciting to play against Barcelona," he said. "This is why I joined the club. If called upon to play in that game, it will be fantastic."