Jensen has been out of action since September with his groin problem.
“Brian had an injection in his groin which will put him back four to six weeks but hopefully that will get to the heart of the problem and he will be back with us,” said Burnley boss Eddie Howe to the club’s official website.
“It’s been a nasty one for him. He had got to the stage where he could do everything bar the long kicking.
“He just felt little twinges in his groin and we felt we had to get it seen to so he’s been to see the specialist and hopefully that’s sorted it.”