Dempsey was subbed from the field during the opening quarter of Sunday’s loss to Collingwood, and the Bombers were initially hopeful the injury was not a complete tear.
But football operations manager Steve Alessio told essendonfc.com.au the 25-year-old would miss the next month of football.
"We sent him for a scan to nail exactly what it is and unfortunately we got what was probably the worst result we could have had," Alessio said.
"He has got a tear in his hamstring tendon and unfortunately that will mean he is going to be out for at least four weeks."
The injury places serious doubt on whether Dempsey will play again this season.
"We are just going to have to go really conservatively with Courtenay and see how he comes up," Alessio said.
He said that while Dempsey would be a big loss it provided an opportunity for others to step up.
"We have seen this year how well Courtenay has played; he has provided significant run off the half back line for us.
"He is really important in our game in regards to the transition of our ball from back to forward and he will be a significant loss."
"What it means is that it is a great opportunity… one goes down and it provides an opportunity for someone else to step up especially at this time of year it is pretty exciting."
The 25-year-old missed three matches earlier this season after suffering a heavy knock against the Sydney Swans in round 10.
