The Hull City player, signed from Norwich City in June for £7m, dislocated a kneecap and damaged ligaments during his new club's opening Barclays Premier League match against Queen's Park Rangers at Loftus Road on Saturday and has been told by doctors that he will have to undergo an operation to rebuild his entire knee. He will miss Scotland's opening four European Championship qualifying fixtures in addition to the friendly with England at Hampden Park in November.
The loss of Snodgrass is a major blow to Strachan - who will also be without the Celtic captain, Scott Brown, for his side's first Euro 2016 Group D encounter with Germany in Dortmund as he recovers from a hamstring injury picked up in pre-season.
Strachan does not have his problems to seek in midfield, with James Morrison of West Bromwich Albion also out of commission at the moment in the wake of knee surgery. He is unlikely to be ready for the meeting with Germany on September 7.
The Scotland manager's focus was on Snodgrass last night, though, and he has backed the former Livingston player to show his professional and personal qualities by returning strongly to reclaim his place in dark blue.
"I am disappointed as Scotland coach and I am disappointed for Steve Bruce [the manager] at Hull City, but, above all, I am hugely disappointed for Robert because I know how much football means to him, nothing more so than playing for his country," said Strachan. "Robert has given everything to become the influential player he is, in the Barclays Premier League and in international football. He is a popular guy around the squad, has a first-class attitude and a work rate that has taken him to the level he has attained.
"It's a shame that this terrible injury has occurred at the start of a new season, with a new club and a new qualifying campaign to look forward to, but the best players overcome such adversity in the long run and I have no doubts Robert will do just that. We will miss him as a group for these qualifiers, but we also know that he will be willing us on to do well."
Bruce has branded Snodgrass' weekend misfortune as "a tragedy". "The diagnosis is he'll be gone for six months which is a big blow to us," the Hull manager added. "It's a tragedy for him and for us."
Snodgrass had become an integral figure in Strachan's Scotland side and comments from Alan Irvine, the West Brom manager, do not inspire any great confidence in Morrison's availability for the meeting with the World Cup holders next month.
Irvine concedes he has no idea when the 28-year-old will be available to play at club level because of his basic lack of fitness. "It's a big concern that Morrison hasn't trained all summer," admitted Irvine.
"He's an important player for us and we could have done with him being with us for pre-season. Unfortunately, he had an operation just before pre-season started and, sadly, it has taken him an awful lot longer to get back than had been anticipated.
"Clearly, when you miss a pre-season, it becomes difficult to catch up. He joined in during the early part of training on Friday, but I think I could have taken part in that part of training.
"After that, he went away and did his own work. The boys that have done pre-season have been in for five-and-a-half weeks and there isn't a short cut to getting fit and ready for games.
"He's a fit lad, which is a real bonus. But it's going to be a big, big task for him to get up to his maximum condition quickly."