The 21-year-old midfielder had to be given oxygen prior to being taken to hospital after colliding with Stephen Ward and falling awkwardly, in the first-half of the match at Turf Moor.
And manager Mauricio Pochettino revealed that the young player will almost certainly miss the rest of the current campaign.
“We hope it's not a big issue but it will be difficult to play again this season. He twisted his ankle but we need to see the scan and then start his recovery,” said Pochettino.
“He is doing another scan (today). In that moment we will see his real problem.”
The news will come as a desperate blow to Winks, who has impressed for Tottenham since breaking into their first-team at the start of the season.
He was making his third league start of the current campaign against Burnley, having recently been handed his first England U21 cap by Aidy Boothroyd.
Spurs however hope to welcome back Victor Wanyama – who was also forced off through injury against Burnley – for their midweek match against Swansea.
Winks joins Tottenham’s growing injury list, with Harry Kane, Danny Rose and Erik Lamela all sidelined.Reuse content