Draper missed Saturday night's 32-point loss to Fremantle in Perth with the injury, and he's no guarantee to return for next week's clash with Port Adelaide at the MCG.
In Draper's absence, Andrew Phillips and Nick Bryan battled manfully against Sean Darcy in the ruck, but the Dockers ended up scoring eight goals from stoppages in what proved to be the crucial aspect of the game.
A fully fit Draper would be a crucial boost to Essendon's finals hopes, but Scott isn't going to rush the 24-year-old back until he's ready.
"It's a really hard one because we don't have a time frame on it," Scott said.
"It's not long term. It's mostly me on this one, because it's not like he couldn't play.
"But he'd be struggling with it. And at round 15, are we just going to have him gradually sort of fall off the cliff slowly over the course of the year?
"The medical staff said, 'look, we can push him and he can play'.
"And I'm saying, 'we're not doing that'.
"So we just want to get him right. And if that takes one week, fantastic. If it takes longer than that, we'll just assess it week by week."
When asked if Draper would miss the Port clash, Scott replied: "These things can turn around really quickly. So I'm just guided by the medical staff.
"But what I won't put up with is, 'look, he can get out there but he won't be at his best'.
"It's just a flat no, and that's been our philosophy all year."
Defender Brandon Zerk-Thatcher is also in doubt to face the Power after suffering adductor tightness against Fremantle.
Zerk-Thatcher was left dazed in the third quarter after being accidentally cleaned up by a teammate, but it was only when he returned in the final term that his adductor flared.
Saturday's 14.9 (93) to 9.7 (61) defeat to Fremantle snapped Essendon's four-match winning run and denied the Bombers (8-6) the chance to jump to equal fourth.
Essendon's loss meant that teams coming off the bye this season have now compiled a collective 1-8 record in their first game back.
Only St Kilda have posted a win straight after a bye so far this season, and that came against a Sydney outfit who also had a bye the previous week.
"You think you'd have the physical preparation but there's something to be said for continuity," Scott replied when asked about teams struggling after the bye.
"And, you know, there's also something to be said for randomness.
"If you want weird, I mean how does a team that's 15th on the ladder (Sydney) kick over 200 points in a game?"
17°C