The 25-year-old centre suffered ligament damage during Scotland's 22-13 loss at Murrayfield to Ireland.
"Huw Jones is unlikely to play any further part in the 2019 Six Nations," said a Scottish Rugby statement.
"Scan results suggest the injury recovery time would likely be beyond the reaches of the current campaign."
With Jones out, Scotland's coaches are sweating on the fitness of the full-back Stuart Hogg. The 26-year-old suffered shoulder ligament damage in the same game.
Hogg is likely to miss Scotland's third game of the championships against France on 23 February at the Stade de France.