The Dutchman went off injured during Edinburgh's RaboDirect Pro12 win over Treviso on Friday night and tests have shown serious damage.
Visser wrote on his official Twitter account: "So the bad news is that I broke my Fibula and damaged some ligaments. Operation soon and hopefully be back in three to four months."
Edinburgh confirmed the player had suffered ankle ligament damage, which will require surgery to repair, as well as the shin bone fracture.
The loss of Visser for the viagogo Autumn Tests against Japan, South Africa and Australia in November is a major blow for Scotland head coach Scott Johnson.
The Dutchman has notched six tries in hist first 12 internationals after qualifying for Scotland under the three-year residency rule.
Visser is also likely to miss the start of the RBS 6 Nations campaign. Scotland kick off against Ireland on February 2 before hosting England six days later. They then host Italy in February before closing their campaign against France and Wales in March.
The 26-year-old's injury is an even more significant blow to Edinburgh - Visser has been the top try scorer in the league for four consecutive seasons.
Edinburgh head coach Alan Solomons said: "This is really disappointing news for Tim. We're very sorry he'll miss the viagogo Autumn Tests.
"He's an asset for Edinburgh Rugby and Scotland. We all wish him a speedy recovery and look forward to seeing him back scoring tries again soon."
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- Edinburgh Rugby