Burke has joined Oli McBurnie and Billy Sharp in having his season ended, in his case by a broken foot. Ethan Ampadu and Jack O'Connell are likely to be in the same both, and Sander Berge may well be too.
The relegated Blades are into the final straight of a debilitating Premier League season, playing at Everton on Sunday and Newcastle United on Wednesday before completing their programme at home to Burnley on May 23.
"Burkey's got a fracture in his foot which will put him out for the season, Sander's picked up a little niggle in the last game so we'll have to assess it but we won't take any risks there," said Heckingbottom.
"We'll just have to see how that goes.
"You want everyone fit and available but we've not got that. We roll with it, we get other people in the team and working towards the next game.
"It's the biggest correlation ever that a team struggling, injuries always spike. It's chicken and egg. I'm not too sure if the injuries lead to the dip in results or the results lead to the injuries with the mental aspect of it.
"We've certainly got a good list of injuries and significant injuries at that. We've had quite a lot of surgery this season and it's one of those seasons where nothing's gone right in that respect."
Berge made his first start of 2021 against Crystal Palace last week, having returned from hamstring surgery as a substitute against Tottenham Hotspur the previous week.
The Norway midfielder will either be a key player last season or more likely their most saleable asset as they look to bridge the financial gap between the Premier League and Championship.
"Let me stress it's nothing to do with his injury previously, the significant hamstring injury he had surgery on, that's 100 per cent fine but the nature of being out for so long and pushing himself to get back fit, he's picked up a natural little niggle," said Heckingbottom.
"If he is fit, fine, no problem but at this stage of the season with where we are and the fact he's been out for such a long period of time, come back and worked so hard to get back, we won't risk him between now and the end of the season."
On the extent of Burke's injury, he added: "Whenever you get a fracture in the foot they can be straight-forward, stick a boot on and they heal naturally or there's ones where you need intervention, you need surgery and pins, things like that. We'll be led by the medical team on that."
Ampadu, on loan from Chelsea, has been managing a pelvic issue this season, but it has got the better of him recently, missing the previous three games and in all likelihood the next three as well.
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