England international Makinson made his return from a two-match absence in Friday’s Challenge Cup quarter-final against Huddersfield but hobbled off after just three minutes.
Saints coach Kristian Woolf said: “It is not quite the same injury as what he has just come back from but it is in a similar area.
“Overall, the news is pretty positive considering what we thought he might have done and what it has ended up being.
“That is going to be in the vicinity of two to four weeks.”
Woolf says second-rower James Bentley is expected to be sidelined for around 14 weeks as he recovers from surgery on a broken leg but prop Louie McCarthy-Scarsbrook will be fit to face Salford on Monday after coming off with a head injury in the win over Huddersfield.
And Woolf confirmed that loose forward Morgan Knowles is set to make his first appearance of the season in that match after recovering from thumb surgery.
Woolf said: “I have no concerns over Morgan’s fitness and physicality and how he will play his first game.
“He is a special player in that sense in that there are not too many who work as hard and play with that level of intensity and toughness.
“Although he has not been able to do all pre-season, it is his thumb that has had surgery on, so he has been able to do all the running.”