Tagovailoa suffered the injury during last night's win over the Volunteers. He had surgery Sunday morning.
"Our physicians performed a successful tight-rope procedure on his right ankle this morning," Alabama coach Nick Saban said in a statement. "This is the same injury, but the opposite ankle that Tua injured last season. Tua will miss next week's game against Arkansas, but we expect a full and speedy recovery."
Tagovailoa, who currently leads the FBS in QBR (95.6), has thrown 27 touchdowns and just two interceptions.
The junior from Hawaii had the "tightrope" procedure on his other ankle following the SEC Championship Game last season and returned in time to compete in the College Football Playoff.
Dr. Norman Waldrop, who was part of the team that performed the procedure on Tagovailoa a year ago, explained how it creates a more stable ankle and allows the ligaments to heal in their natural position.
"What we do is we drill a hole from the fibula into the tibia and cast these tightropes through the bone and synch it down and tighten it," Waldrop told ESPN in 2018.
"What these tightropes do are stabilize the ankle. It holds that little bone in its home. It holds it still and stable enough that the bones don't want to spread apart."
With Tagovailoa sidelined, Alabama will once again turn to former backup Mac Jones. The redshirt sophomore from Florida came on in relief of Tagovailoa against Tennessee and completed 6 of 11 pass attempts for 72 yards, no touchdowns and no interceptions.
No. 1-ranked Alabama hosts Arkansas on Saturday. It will then have the week off before No. 2 LSU comes to Tuscaloosa.
A year ago, after Tagovailoa had the same surgery on his left ankle, it was 13 days before he returned to practice, and even then it was on a limited basis.
Tagovailoa suffered the injury on Dec. 1 in the SEC championship game win over Georgia, and the College Football Playoff semifinal game against Oklahoma was on Dec. 29. Tagovailoa acknowledged going into that game that he wasn't 100 percent and probably only "80 to 85 percent."
The LSU game this year (Nov. 9) would be 20 days after Tagovailoa's latest surgery, which is seven days earlier than he returned to play a year ago against Oklahoma. The recovery didn't seem to hurt Tagovailoa against the Sooners. He was 24 of 27 for 318 yards and four touchdowns.