The defender, 27, was carried off after he was injured in an 85th-minute collision with opponent Theo Hernandez.
Barcelona said on Saturday evening that Vidal, signed from Sevilla in 2015, would be out of action for five months.
"Aleix, you'll be back stronger - get well soon," wrote team-mate Andre Gomes on Twitter.
Vidal had recently established himself as a regular in Luis Enrique's side, scoring in league victories over Las Palmas and Athletic Bilbao since the turn of the year.
After suffering his injury, he was taken to hospital in the Basque city of Vitoria-Gasteiz, where Alaves are based, for an operation to reduce the swelling on his ankle.
His was one of two serious injuries sustained in La Liga matches on Saturday; Osasuna defender Tano Bonnin broke his leg during the first half of their 3-1 defeat at home by Real Madrid.
Barcelona full-back Aleix Vidal will miss the rest of the season after dislocating his right ankle during Saturday's 6-0 La Liga win at Alaves.