The 25-year-old had an MRI scan earlier this week and it confirmed he has suffered ligament damage in his elbow.
Scott said: "Thanks to those who have sent me nice messages, really appreciated. I'm gutted of course with the injury; hopefully I will be back before the end of the season."
Scott, who has won 34 caps, started in Scotland's opening Six Nations game against England before dropping out of the team for the match with Italy.
In a statement earlier this week, the Scottish Rugby Union said: "An MRI scan at Spire Murrayfield Hospital on Monday confirmed that Scott sustained elbow ligament damage in his club's GUINNESS PRO12 loss to Connacht on Friday.
"Further examination this Friday will confirm if the player requires surgery on the joint.
"However, it is clear at this stage that he will at least miss the remainder of the 2016 RBS Six Nations, and will return to his club for ongoing care and assessment."
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