The Belgium defender was substituted only minutes after coming on as a half-time replacement for Steven Caulker when he landed awkwardly.
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Villas-Boas told reporters: "There is some range of movement so we have to hope it won't be that long. Hopefully he'll be back for the first game of the season.
"He might have sprained the ligaments in his left ankle. He will need to have an MRI scan to establish full extent."
Vertonghen, meanwhile, tweeted after the match: "Let's hope the injury isn't to bad. Scan tomorrow morning. Thx for your messages!"
Kick-off in Hong Kong was delayed for 30 minutes due to a waterlogged pitch and the two sides subsequently agreed to play 40-minute halves as Paolo Di Canio's side emerged 3-1 victors.