Slade sustained the injury, as well as ankle damage, during his side's 41-27 win over Wasps on Saturday.
Slade, 22, had a plate and wiring inserted during what Exeter coach Rob Baxter described as "a pretty major operation".
"You would normally talk around four months for an injury like this," Baxter told the club's website (www.exeterchiefs.co.uk.)
"We are certainly not pencilling in any date for Henry's return because we know it is long-term. We will start talking about a return date in eight to 10 weeks' time when we know a bit more -- it will take a bit of time though and a lengthy rehab process."
Slade made his England debut in a World Cup warm-up against France in August but was overlooked by coach Stuart Lancaster during the tournament until the dead rubber victory over Uruguay when he scored a try in a 60-3 victory.
The creative centre was expected to push for a starting berth under new coach Eddie Jones but will now have to wait until the tour of Australia in June to revive his international career as England's midfield problems show no sign of ending.
England kick off their Six Nations campaign in Scotland on Feb. 6 and play their final game in France on March 19
(Editing by Ed Osmond)
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