Early indications had been that Visser, who was taken off after just 22 minutes of a match that Edinburgh went on to win 20-13, may only have suffered a nasty ankle sprain, but an X-ray has revealed that the 26-year-old actually suffered a fractured fibula. To make matters worse, another scan revealed that he had also suffered ankle ligament damage, and will now have to undergo an operation.
A more detailed prognosis will become available after that procedure, but the best prediction at the moment is that Visser will be out of action for between three and four months. Scotland begin their RBS 6 Nations programme against Ireland in Dublin on February 2, and their series ends against Wales in Cardiff on March 15.
"This is really disappointing news for Tim," said Edinburgh head coach Alan Solomons. "He's an asset for Edinburgh and Scotland. We wish him a speedy recovery and look forward to seeing him back scoring tries again soon."
The Dutch-born Visser had already set a number of Celtic rugby scoring records before he became eligible for Scotland on residence grounds in June 2012. A few days later, he made his international debut against Fiji, marking the occasion by scoring a brace of tries. He also scored two on his first Test appearance at Murrayfield, against the touring All Blacks last November. In just 12 matches, he has now scored six times, a rate of return far in excess of what most other Scottish players have achieved in his position in recent times.
Visser's last try for Scotland was in the Six Nations loss to France in Paris last March. His form on the summer tour to South Africa was unimpressive, but he had shown glimpses of his old self in Edinburgh colours recently. Ironically, the player who could stand to benefit from his misfortune is Max Evans, whose own Scotland career stalled around the time of Visser's emergence.
Evans was left off the South Africa tour on the basis that it was primarily a development exercise, the interim head coach Scott Johnson explaining at the time that he knew everything he needed to know about the player's abilities. However, most observers believed Evans had been snubbed, and that his Scotland days were numbered.
"It was a little bit of a shock," said Evans, who was taking part in Scotland's autumn training camp in Glasgow yesterday. "Although I didn't feature much in the Six Nations, I was on the bench for every game and came on against the French at the end - when I felt I performed well. But Johnno had his reasons, which were fair enough. A few young guys he wanted to have a look at and also, more importantly, give me a good off-season and a good pre-season."
Evans' omission from the summer tour seemed even more questionable as he had just helped Castres secure the French Top 14 title. He has also been in impressive form for his club side this season.
As well as form, Evans has versatility on his side. He can play on the wing, but around a third of his 35 Test apperances have been at outside centre. With Stuart Hogg and Peter Murchie also ruled out by injuries at the moment, Johnson is likely to pick Sean Maitland at full-back, leaving a number of possible permutations of players in the three-quarter line.
Should Johnson prefer Sean Lamont or Tommy Seymour on the wing then Evans could be deployed in the midfield. For his part, the 30-year-old is keen to explore that avenue as well.
Evans said: "I've had words with the coaches that I have now [at Castres] and they definitely have it in their mind to play me in the centre for certain games. I think I'm one of those players who can do both and it just so happens I have been playing wing more regularly recently.
"So, I'm easy - but one thing I would like is more game time at 13. I played there in pre-season but haven't had any time there in the league. It would be nice to get a couple of games under my belt there before going into an international there - but I can't really see that happening."
Niggles and strains meant that a number of players sat out yesterday's session at Scotstoun. Evans was one of those whose training was curtailed, as were Jim Hamilton, Seymour, Euan Murray, and Alex Dunbar.
Niko Matawalu, the Glasgow scrum-half who has been accused of biting an opponent during last Friday's PRO12 match with Munster at Scotstoun, will have his case heard at a PRO12 disciplinary hearing in Cardiff today. Munster's Conor Murray will answer a charge of striking an opponent with his elbow at the same hearing.