Haining was the third different No 6 to be used by Scotland in the championship this season when he started against France but the Edinburgh player will not be involved in the game in Rome next Saturday.
“It’s his shoulder, his AC joint,” said Mike Blair, the Edinburgh coach. “We’re not too sure the length on that but it’ll be weeks rather than months.”
Scotland are already without Jamie Ritchie for the rest of the season due to a hamstring tear and Matt Fagerson injured his foot against France. Hamish Watson missed the French game after returning a positive Covid test.
Rory Darge stepped up and made his first Scotland start against France and looks set to play against Italy next weekend.
Blair, meanwhile, praised the performance of his Edinburgh side as they thrashed Connacht 56-8 in the United Rugby Championship at the DAM Health Stadium.
Missing 14 internationals in their pack - including Haining - the capital club impressed with eight tries against their Irish visitors.
Blair singled out full-back Henry Immelman, who scored two tries, and compared him to Gavin Hastings. “I thought Henry was outstanding,” said Blair. “I remember at the start of the season I likened him to Gavin Hastings as he is that sort of big, powerful kind of man who is solid and reliable.
“I was also impressed by Ben Muncaster and Conor Boyle and Angus Williams at tighthead, as well as Blair Kinghorn at ten. For someone who had had a difficult five, six week period away with Scotland, back with us, away with Scotland, Blair stood up really well and led the team really well.
“I find it strange that people challenge what Blair can do as 10, especially if they’ve watched Edinburgh this season because he’s got a real understanding of where space is and he communicates that. He’s got brilliant soft skills as we saw with his offload to Emiliano Boffelli for the first try.
“I’m really confident in what we’re trying to do with Blair and was really confident that he was going to play well on the night and he did.”