The reigning Giro d’Italia champion went down on the approach to the final climb of the day, while descending near the front of the bunch.
Geoghegan Hart went down as the peloton descended from Mont Brouilly around 20km from the finish in Chiroubles, as he lost traction on a right hand bend and the wheels slid out from under him.
After bouncing up and quickly rejoining the bunch, Geoghegan Hart sat up shortly after.
The Ineos Grenadiers rider was then forced to leave the race, organisers confirmed shortly after.
In a statement on social media, Ineos Grenadiers said: “Not our race this year. Sadly stage four concludes at Paris-Nice without Tao Geoghegan Hart.
“The young Brit was forced to abandon following a crash in the closing kilometres.
“He will now head to hospital for further assessment. Medical update to follow later.”
Ineos sports director Gabriel Rasch said: “On the descent his front wheel slipped in the corner. He was in fourth position.
“It was really bad luck. I don’t know if there was some gravel or why he slipped.
“He landed on his face, head and knee pretty badly and he felt a bit dizzy. We thought it was the right decision to stop him.”
Rasch added: “[The rest of the team] waited at the back of the peloton until they saw what state Tao was on.
“I told them to carry on and do their very best.”
Ineos have suffered a tough opening four stages to the 2021 Paris-Nice, after Richie Porte was forced to abandon following a crash on stage one.
Geoghegan Hart stayed out of trouble on the opening two sprint stages, but slipped back in the general classification in the individual time trial on stage three.
The best-placed rider overall for Ineos in Paris-Nice is now Dylan van Baarle in 19th-place, 1-43 down on the race leader.