The National League Cup tie was abandoned due to the seriousness of the injury as Kone received treatment for 15 minutes on the pitch.
The Mali international was floored after a head collision in United's penalty box at the Lamb Ground.
Kone, 19, was eventually taken off the pitch on a stretcher with a mask on his face.
Later in the evening, the game was abandoned after it was initially suspended. Further, United released a statement to deliver a positive update: "We can confirm Sekou is conscious, stable and communicating with United’s medical team.
"He has been taken to hospital, as a precaution, for further checks. Everybody at the club wishes him a speedy recovery."
Tamworth also stated: “Due to the medical situation, we are forced to abandon tonight’s fixture, details will be revealed in due course. We would like to wish safe travels to all the Man United fans, staff and players. We especially wish Sékou Koné a speedy recovery.”