The 28-year-old captained Wales in the absence of Sam Warburton, but was forced out of the pre-tour game after just 23 minutes at Twickenham.
And with surgery rehabilitation required, Lydiate may be forced into a race to be fit for the start of the Guinness PRO12 season in September, according to Ospreys senior physiotherapist Anthony Carter.
"Dan sustained a significant injury to the AC joint in his right shoulder, caused by an impact during the England game on Sunday," he said.
"He's been seen by Richard Evans, shoulder specialist at Spire Cardiff, who confirmed that the shoulder requires stabilisation via surgery, after which there is an expected rehab period of 12-14 weeks."
Despite the injury, Wales are taking nine from Lydiate's region to the Antipodes, with the man himself replaced by Cardiff Blues' Ellis Jenkins, who signed a new long-term contract back in December to keep him at Cardiff Arms Park for the foreseeable future.
There was some good news for Ospreys however, with lock Lloyd Ashley triggering a three-year contract extension to become the 16th player from the region to sign on for next year since December.
Ashley skippered Ospreys in the absence of Alun Wyn Jones last season after coming through the academy system at the Liberty Stadium.
"It's my home region, where I've grown up, and it's an honour to be able to sign up for three more years" he said.
"Like any season, last year was a huge rollercoaster, both for me personally and for the Ospreys as a team.
"Despite the disappointment and frustration, we can look back at the season as one that gives us something to build on, where we showed what we can do despite being a young group."
Ospreys head coach Steve Tandy also praised the unseen work of Ashley, citing him as an integral part of the squad after making his 50th appearance in last season's home opener against Munster.
"Lloyd is Mr Consistent for us," he said.
"He doesn't get the credit he deserves outside of our environment but he's consistent, he's diligent in everything he does and has the respect of everybody here, youngsters on the development pathway and senior internationals alike.
"When you look at his numbers, his phenomenal workload is clear, with the number of tackles he is making and the strength of his carrying, and it was a real blow for us to lose him to injury like we did in the Exeter game."
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