Thomas suffered the injury with 5:21 left in the third quarter while making a block in Sunday's game as the Tennessee Titans kept the Browns winless with a 12-9 victory in overtime.
"MRI reveals torn tricep tendon. Surgery soon. Tough break," Thomas tweeted Monday.
Thomas never missed a snap in his NFL career prior to the injury. He was the third-overall pick out of Wisconsin in the 2007 draft and has played 10,363 consecutive snaps over 10-plus seasons.
Thomas will miss this Sunday's game against the Minnesota Vikings in London that will also end his streak of 167 straight starts.
"I've done it a million times where you're just blocking a guy and you go try to finish him and you get one last shove, one last push, and just felt something unnatural in your arm," Thomas told reporters after Sunday's game.
"It wasn't an infinity streak. There was certainly going to be a time where either because of injury or lack of production it was going to end. I think I was enough of a realist to understand that I wasn't going to be able to continue on forever without missing a play. It was just a matter of time, and unfortunately it happened in Week 7."
After undergoing the MRI exam on Monday, Thomas showed his sense of humor: "The Geneva convention on torture (confinement, stress positions) was just violated when they wedged me into that MRI tube for 2 hrs. Yikes!"
Thomas rolled to the ground in pain after a short run play against the Titans. His teammates knelt and watched as trainers tended to him, thinking he would stand and walk back to the huddle as he always does. But not this time.
Thomas left the game to a standing ovation before trotting to the locker room.
Browns coach Hue Jackson went out on the field to show his support.
"(I told him) that I love him and I appreciate everything that he is," Jackson said after the game. "I promised him that when he's back, if he's back, that we're going to get this thing figured out because he is Cleveland Browns football. He is a guy that keeps us all going and moving forward. We owe him more than what we have given him thus far. That is for sure."