Thomas was involved in the first major crash of the race that included teammate Luke Rowe and Alberto Contador (Tinkoff) and the Welshman was caught up due to another fall at the line. The second incident was the more serious, with the Paris-Nice winner crashing and his stem hitting him in the chest.
No x-rays were needed but Thomas has been suffering with pain in his ribs. It is affecting both his breathing and riding style.
"It's still pretty sore to be honest and it will take a few days to get over but it should be all right," Thomas told Cyclingnews on stage 3.
"I landed on my stem and got a bruise from there and on my ribs, which I have taped up. It affects my breathing and when I'm getting out of the saddle, so when I cough or tense my stomach it hurts."
Despite the falls and already losing time in the race, Thomas is riding on. He had a tough Tour de Suisse just before the Tour de France and admitted that his pre-Tour aims of a high GC finish would be shelved as he looked to help team leader Chris Froome win his third title.
"I've certainly had a lot worse," he said stoically.
Team Sky boss Dave Brailsford echoed Thomas' words. "We didn't think it had been fractured but it's a muscular pain," he told Cyclingnews. "He's hurt his ribs quite badly in the crash the other day and it's quite sore but he's done pretty well and is there or thereabouts."
Brailsord also added that Thomas had been through and survived worse during the Tour de France. In 2013 he broke his pelvis on stage 4 but rode on and finished the race, helping Froome to his first Tour title.
"He's a tough guy," said Brailsford. "When the guys went into the barriers, he went into them and I think his stem hit him in the chest. He's a tough guy, though, and if he can ride around with a fractured pelvis then he can ride around after a whack in the ribs."