The 18-year-old came on as a substitute during Saturday's 1-1 draw with West Ham at Ewood Park but lasted only 10 minutes before hobbling off after falling awkwardly in a challenge with Carlton Cole.
Kean confirmed that Jones, who is considered one of England's brightest prospects, has suffered a serious knee injury, while Jason Roberts damaged a hamstring and Christopher Samba was also forced off.
"I think Phil Jones is going to be a long-term one," said Kean. "He's got quite a bad knee injury, it'll probably be four or five months, which is terrible.
"He'll have an examination in the morning and probably have surgery in the morning, too. Jason Roberts has picked up a hamstring injury. We don't think Chris Samba is as bad, it's a slight twist in his ankle."
Source: PA
Source: PA