The newspaper reported that an MRI exam on Thursday revealed the injury, which Tkachuk suffered on Oct. 15 after he hit himself in the midsection with the butt of his hockey stick.
Tkachuk was placed on the seven-day injured-reserve last week and has not skated since Monday, when he tested the injury but still experienced soreness in his midsection.
"Time-wise, nobody knows," Blues GM Larry Pleau told the newspaper. "Three weeks, five weeks ... it's all up to [Tkachuk] and when he's ready. In the meantime, he'll have to take it easy."
"He couldn't do a whole lot," Blues coach Mike Kitchen added. "At least Keith knows what it is now, but it's probably going to take awhile [to get him back]. I think we'll just see how comfortable he gets and how much pain he can put up with. Is it a week? Two weeks? Hopefully it's less than that."
The Blues suspended Tkachuk before the season's start because he reported to camp overweight and failed a physical. He has played two games so far this season after he hurt his groin in the season opener and now the latest injury.
The 33-year-old Tkachuk is the second highest-paid player in the NHL at $7.6 million. He had 33 goals and 38 assists in 2003-04.
Information from The Associated Press was used in this report.