Scotland wing Jones was forced from the field in Saturday night's 32-14 RBS 6 Nations loss to Ireland in Dublin.
The 23-year-old Edinburgh back, who was winning his fourth cap, was taken off following a sickening clash of heads with opposite number Andrew Trimble.
The incident occurred during the 62nd minute when Ireland scrambled furiously inside their own 22, with Jones collapsing instantly from the collision before receiving prompt medical attention.
Scotland team doctor James Robson said on scotlandrugbyteam.org: "Lee took a blow to the head which resulted in a severe concussion.
"He remained in St Vincent's University Hospital, Dublin, overnight in the care of consultant John Ryan.
"He has made good progress overnight and will stay in hospital this morning until the consultant is happy for him to be released. He is scheduled to travel back to Scotland tomorrow.
"We would like to thank John and his team for the expert help given to us."
Jones is now likely to be a major doubt as Scotland travel to Italy next weekend seeking to end a run of six successive Test losses to avoid the wooden spoon.
The Scotland squad are scheduled to return to Edinburgh this afternoon to begin preparations for Rome, with four other players set to require further medical attention.
Two did not complete the game - scrum-half Mike Blair (shoulder), who was replaced by Chris Cusiter, and centre Max Evans (dead leg), who ended the match in the sin bin.
Flanker John Barclay (ribs) and number eight David Denton (shin bruising) will also require further treatment, while a number of other players have what Dr Robson described as "lesser soft-tissue" injuries.
Scotland head coach Andy Robinson is scheduled to name his team for the Italy clash on Wednesday.
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