The prop collided with team-mate Maro Itoje, trying to tackle Makazole Mapimpi, and immediately hit the floor.
There was a lengthy stoppage as the 26-year-old was assessed by the on-duty doctor, before he regained consciousness and walked off the field.
The Harlequins front-row was replaced by 32-year-old Dan Cole.
Sinckler later joined his team-mates on the sidelines after the break but head coach Eddie Jones said the forward “will go through all the head injury protocol”.
“You have 23 guys, you lose a guy early and you have got to be able to cover it,” said Jones.
“I don’t think that was a significant factor in the game.”
South African hooker Mbongeni Mbonambi was also taken off for a head injury assessment after being replaced by Malcolm Marx in the first half.
The forward did not return to the field and said he “understands” why he was “forced off” despite not wanting to leave the field.
“I had concussion,” Mbonambi said. “I was arguing with the doctor and I was trying to get the last 20 minutes in because it’s a World Cup final.
“But when a medical team makes a call, you have to respect it.”
