The 21-year-old, who has made 15 appearances for Fulham this season, is Sean Dyche's first signing as Burnley manager.
Sweden international Kacaniklic spent time playing under Dyche during a loan spell at Watford last season.
"He is an exciting young prospect and something different to what we have, which is important. He's dynamic and can mix up his game," Dyche told Burnley's official website.
"He was with us at Watford last year and was then called back and went into Fulham's first team, which is obviously a good sign.
"He has started this season in the Premier League and got himself a couple of goals. It's a good link with Fulham. They know their player was looked after at Watford. He is aware of us as a staff and knows he will get looked after here."
Kacaniklic could go straight into the squad for Burnley's trip to Charlton Athletic on Saturday afternoon.