The 33-year-old was taken to hospital after suffering abrasions on his shoulder and a cut above his right eye in the incident on Tuesday's Stage 4 from Murten to Arlesheim. He was withdrawn from the race.
Team Ineos later revealed that Thomas had been given the all-clear and would likely defend his Tour de France title in two weeks' time.
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"Thanks for all your messages!! Gutted to leave but luckily I’m all ok. I hit my head and needed stitches above my eye, so the doctors stopped me getting back on my bike. It just means I’ll need some big training rides next week now." Thomas said in a tweet.
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"There was a lip in the road that came out of nowhere," the Welshman added in a statement. "An Astana rider hit the lip and crashed and I had nowhere to go. I landed on my shoulder and my face and there was quite a bit of blood.
You’ve always got to be cautious with a head injury, and whilst I was keen to carry on, the doctors made the right decision to pull me out of the race.
"Clearly it’s frustrating and a small setback for my Tour de France preparations, but there’s still plenty of time before we start in Brussels in a few weeks' time. We will recalibrate and I’m sure my coach Tim (Kerrison) will have a plan in place to ensure I’m ready for July 6th."
After Chris Froome's terrible crash at the Criterium du Dauphine, Team Ineos could have had further problems if Thomas was also not able to lead their team. However, the Team Ineos doctor, Derick Macleod, backed his rider's assertion that he would make the start date.

He said: "Geraint took a heavy fall. The main area of impact was to his head. He passed his initial concussion roadside test but with the nature and severity of the impact, it was felt unsafe for him to continue in the race.
"He was taken to hospital and thankfully all the X-rays and scans have come back clear. He’s now back in the team hotel and in good spirits."
Macleod added: "He’s been given the all clear which is great but we will continue to monitor him over the next few days. Knowing Geraint, it won’t take him long to get back on his bike but we’ll need to ensure he’s symptom free in the next few days before he does so. We’re optimistic he’ll make a full recovery over the coming days though and all being well he’ll be back on his bike very soon.”