Wells suffered bone bruising in his foot after a training accident in the lead-up to North Melbourne's round five meeting with Collingwood.
While he played in that game, he has been out with the injury since and Kangaroos football manager Geoff Walsh said Wells hadn't responded well when building his rehabilitation program last week.
"The past couple of weeks we've tried to manage that with his training load and be really guided by the symptoms of his pain," Walsh said on Monday.
"Our physio and rehab team tried to step that up last week and pour some more running into him and he didn't react well to that.
"Since that, further subsequent investigation shows the ligament in the foot hasn't really responded to the rest or the treatment like we would have hoped.
"We're going to pull back from the running for a couple of weeks so that will probably mean I would say three-to-four weeks on the sidelines as of today, which is disappointing but we think the best way to respond to it."
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Scans last week revealed "a little bit of a grey area" but not a fracture, and Walsh said Wells wouldn't need surgery. He will resume training in two weeks.
Wells' durability has been terrific throughout his AFL career, playing 19 or more games over the previous four seasons.
"He's a player, like all players, they just want to play, don't they?" Walsh said.
"And a player of Daniel's calibre, we'd love to see him play too. He's a bit frustrated but he understands there's probably no other course of action at this stage because it hasn't responded to what we'd been applying to date."
The Roos beat the Brisbane Lions by 87 points on Saturday night and face Geelong, West Coast (Patersons Stadium), Richmond and Adelaide (Adelaide Oval) in the next four weeks.
