The injury happened in the first half of Saturday's 3-3 road draw against the Philadelphia Union.
The team said the 34-year-old DeMerit will rehab the ankle instead of opting for surgery.
The veteran defender tore his left Achilles tendon in the first game of the 2013 season and missed six months of action.
Vancouver is 5-2-6 in Major League Soccer so far in 2014 — with DeMerit having started 11 of those matches — but the Whitecaps have allowed an average of more than 1.5 goals against per game.
Vancouver's next game is June 25 at home against the Montreal Impact.