The powerful defender copped a knock to the knee during the opening minutes of the match.
He had his leg strapped up and briefly returned to the field, but was subbed out during the second quarter.
Hurn was later diagnosed as having a minor medial ligament strain.
"He might be two to three weeks," West Coast coach Adam Simpson said after the game.
Although his men demolished Melbourne by 93 points, Simpson described the match as "frustrating".
But he added: "We're obviously happy with the scoreboard result. We've started well two weeks in a row now, so we'll take that with us."
The Eagles' new coach, who is yet to taste defeat, was pleased with Nic Naitanui's effort in the ruck and around the ground.
"I think he had 10-odd possessions in the first quarter, and had impact," he said.
In a warning for the rest of the competition, Simpson declared his team has plenty of improvement to come.
"We're still not quite where we want to be with what we've been working on over summer," he said.
"I don’t want to sound disrespectful to Melbourne or the Bulldogs, but there's still things we review that aren't where we want to be.
"Maybe that's just striving for perfection, I don't know. But it's not like we can't play any better.
"Some of our ball-movement stuff … you can tell the players sometimes misread the cues and tempo of the game.
"We're happy. Don't get me wrong. We're pleased with the result and where we are. But it's a long year and we haven't really been thrown in the deep end and tested yet.
"I'm sure that's coming."
The big test is unlikely to come next weekend, with the Eagles hosting St Kilda at Patersons Stadium on Saturday evening.
But Simpson wasn't about to play down the clash with the Saints.
"It's a six-day break, they're two and zip as well, so we've had a quick look at them yesterday and they'd be pretty happy with their start as well," he said.