The Belgian star was forced off just before half time in the 3-1 defeat at Southampton, after pulling up five minutes before the break when clearing the ball out of play.
Sean Dyche will await further news on the midfielder’s diagnosis, but it will be a major concern for the manager, with the Clarets facing a tough run of matches in the coming weeks.
Burnley will entertain in-form Everton next weekend, before travelling to Manchester United on October 29 and then hosting Crystal Palace before the next international break.
Defour has been an influential figure since his summer switch from Anderlecht, with one goal and three assists so far this season and Burnley will hope the injury concerns are not as bad as first feared.
A goal apiece from James Tomkins and Luka Milivojevic handed Crystal Palace a crucial 2-0 win over Huddersfield at the John Smith's Stadium on Saturday evening.
Manchester United bounced back from their Champions League exit as they beat Brighton 2-0 at Old Trafford on Saturday night to reach the FA Cup semi-finals.
Tottenham reached the FA Cup semi-finals after they cruised to a 3-0 victory over Swansea in their quarter-final clash at the Liberty Stadium on Saturday.
Premier League basement club West Brom squandered the lead as they suffered a 2-1 defeat to Bournemouth at the Vitality Stadium on Saturday.
Chesterfield boss Jack Lester felt his side were unlucky not to claim all three points after their 1-1 draw at Cheltenham.
New Swindon manager Phil Brown revelled in his side's victory at Cambridge in his first game in charge.