The 22-year-old sustained the injury in the club's 3-2 defeat to Aston Villa during the week, and Pochettino admits that he is unsure as to when the former Celtic star can resume first-team duties.
Speaking to reporters, the coach said: "Victor has a hairline fracture [in his leg].
"We don't know time-wise how long he is going to be because it also depends on personal recovery times.
"I hope he recovers soon. Right now, we don't know exactly when."
The Kenyan has established himself as a key figure for the Saints since securing a £12m switch to St Mary's Stadium from the Scottish champions in the summer.