The 25-year-old suffered ligament damage during Saturday's 22-13 loss at Murrayfield.
"Scotland centre Huw Jones is unlikely to play any further part in the 2019 Six Nations," said a Scottish Rugby statement.
"The Glasgow Warriors midfielder sustained knee ligament damage in
the national team's round two defeat to Ireland at Murrayfield Stadium
on Saturday, with scan results suggesting the injury recovery time would
likely be beyond the reaches of the current campaign."
Fullback Stuart Hogg suffered shoulder ligament damage in the same game.
The statement said Hogg was under the joint care of the Glasgow and
Scotland medical teams, "with his rehabilitation progress and review