Former Lincoln City and Halifax striker Burrow tore his calf during the Pilgrims' 4-1 FA Trophy victory over Kidderminster Harriers before Christmas.
"Jordan Burrow is looking a really bad one, to be honest," Elliott said.
"He'll do well to get back for the later stage of the season."
Target man Burrow, who has scored 5 times in 24 appearances this campaign, was forming a formidable partnership with his old Gateshead and York City teammate Jake Wright jnr.
"He's been brilliant, he's been in great form and the front two were looking the real deal up there," Elliott continued.
"I was enjoying what they were about.
"Jordan's not a player you think about getting an injury either. He never goes down in training, never misses a minute of anything.
"I'm really gutted for him."
Adding to the misery, Elliott confirmed that sidelined defender Jake Wright snr could still be looking at a 'couple of months' out of action following a hernia problem.
Winger Jay Roillins, yet to feature this campaign following a knee injury in pre-season, looks likely to be fit to return next month.
Speaking after yesterday's defeat to Brackley Town, Elliott confirmed: "Jay should be the middle of the month.
"He's done a bit (of training) today, felt a bit of a twinge but nothing major."
There could, however, be some good news on the horizon for the Pilgrims ahead of Sunday's arrival of Alfreton Town.
It is hoped midfielder Paul Green will be fit following his hamstring problem, while Scott Duxbury and Peter Crook could be back after suffering from Covid.
"Greeny, I hope, should be back for the weekend," Elliott added.
"As long as he comes through training on Thursday."
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