The Demons were overpowered and outclassed in the midfield as they slumped to an 18.12 (120) to 8.14 (62) defeat at the MCG on Saturday.
It was their first loss to the Suns since 2014, after a dozen straight wins over the Queensland side.
Lindsay, taken with pick 11 at last year's draft, was hurt during the opening exchanges and was immediately substituted out of the game.
"We'll have to get a scan on that and hopefully it's not too bad," Demons coach Simon Goodwin said.
Pressed on whether Lindsay had suffered damage to his anterior cruciate ligament, Goodwin said he was unsure.
"It's just too early to tell," he said.
"It's not quite clear from a medical perspective and normally you get some pretty good information on that straight away.
"We're unsure, so we need to go and get that scanned."
Melbourne were badly beaten around the ball and blown away by Gold Coast after halftime in a loss that left them at 0-3 for the season.
It is their equal-worst start since 2012 and there is no rest in sight, with a tough trip to face Geelong at GMHBA Stadium in round four.
"You're going to have some challenges at certain times and we're having ours early," Goodwin said.
"But I've got belief in this group and everything that we're capable of.
"You're not seeing it now and our supporters will be disappointed.
"I acknowledge that, that they would be disappointed with where we sit right now.
"But I've got unwavering belief in what we're capable of and we're going to go after delivering it."
Goodwin said Jake Lever (ankle), Caleb Windsor (foot) and Charlie Spargo (concussion) are all in the mix to return next week.
Kysaiah Pickett is available after serving his three-match suspension over a bump on Collingwood's Darcy Moore last August.
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