The Brentford midfielder tumbled from the advertising boards while marking his side's dramatic 3-2 last-16 win over Mexico and had to be stretchered from the pitch.
Tuchel confirmed the extent of the problem afterwards, telling BBC One the timing could hardly have been worse.
"Jordan just fell over and injured his wrist. It looks really bad," said the England boss. "It's quite a serious injury and it doesn't fit with the evening, that Jordan is now not with us. The doctor told me he is in hospital."
The incident unfolded as England players joined supporters behind the goal for a rendition of Oasis' "Wonderwall" moments after the final whistle. Henderson attempted to hop over the hoardings to reach the fans, clipped his foot on the way down and threw out his left arm to break the fall.
Team-mate Dan Burn alerted medical staff, and Henderson was given oxygen before being carried off on a stretcher. Captain Harry Kane played down the incident afterwards, saying only that Henderson had "fallen over" and hurt "something to do with his arm."
The 36-year-old has barely featured in Mexico, with his solitary involvement so far a substitute cameo in the closing stages of the Group L win over Panama, a milestone that made him the first England men's player to appear at four World Cups.
He stayed behind in Mexico City with a member of England's support staff rather than travelling home with the squad, who returned to their Kansas City base.
Should the injury rule him out, Henderson would become the second England player sidelined this tournament, following Reece James, who suffered a hamstring problem in the opening group game.
Jarell Quansah is also unavailable for the next round after being sent off during the win over Mexico.
Tuchel's side now turn their attention to Norway in Saturday's quarter-final in Miami, kicking off at 22:00 BST.