Saad's Gather Round performance against Adelaide last Thursday was brought to an abrupt end due to the hamstring concern, with the club confirming this week the 28-year-old has sustained a low-grade strain.
The dashing defender was among a trio of ailments from Thursday, with fellow backman Mitch McGovern a late out due to calf tightness, while ruckman Marc Pittonet was subbed out of the game against the Crows with an eye injury.
The Blues are hopeful McGovern will be in time for their Round 6 bout with the top-placed Saints, with the tall defender needing to prove his fitness later this week at the club's main session on Friday.
Pittonet has been cleared of any damage to his eye and will be available for selection this weekend.
Midfield-forward duo Jack Martin and David Cuningham will look to return to skills sessions next week as they recover from calf issues, while defender Caleb Marchbank has returned to similar sessions this week after overcoming his own calf injury.
Young pair Matt Cottrell and Jordan Boyd are both nearing returns to action, having resumed full training under Michael Voss after battling foot injuries. Both Cottrell and Boyd are expected to be available for selection next week.