The 21-year-old centre-back will have to undergo a special training programme to cope with the problem.
But the former Rangers and Liverpool player will be able to face Inverness at Tynecastle on Saturday as Hearts bid to wipe out the remainder of their 15-point Scottish Premiership penalty for going into administration.
Manager Gary Locke told Hearts TV: "It's a wee problem Danny's had for a couple of weeks now. His shins were flaring up so we decided it was best to get him a scan. Fortunately it's come back and, while it's not brilliant news, it's certainly better than we anticipated.
"We just have to manage him through the week and wrap him up in cotton wool to make sure he's okay for the games on Saturday.
"He is obviously happy because it could've been a lot worse. It's not ideal but the good thing is we can manage it and we can get him out on the pitch on a Saturday, which is the most important thing."