Evans, the English champions' chief playmaker, limped off after 17 minutes of the 40-13 Heineken Cup victory over Biarritz with his left ankle heavily strapped and was later walking on crutches.
"Nick will have his foot in a boot for a little while and we'll see what it's like," O'Shea said.
"There's no break but there's a little bit of damage. We need to wait 24-48 hours and get it scanned.
"He won't be available against Connacht next Saturday, that's for sure, but it will be weeks rather than months."
An impressive performance by replacement Ben Botica, the 23-year-old son of rugby league great Frano, ensured Evans' absence was barely felt.
Botica kicked 18 points to suggest there is life after Evans should the former New Zealand fly-half - one of Europe's most sought-after players - reject a new contract at Twickenham Stoop.
"Like father like son - his goalkicking is pretty special. He ran the game really well and attacked the line," O'Shea said.
"It was the biggest match he's ever played in, so his performance was a massive, massive plus. Ben was outstanding."
England scrum-half Danny Care was superb, as was number eight Nick Easter whose strong form is generating momentum behind calls for his international return.
"Nick is absolutely magnificent and he will keep on knocking until someone answers," O'Shea said.
"It's great for us but Nick is ambitious and is desperate to play for England.
"The boys are giving him a going-over in the dressing room, saying the England bandwagon has started again."
Tries from Danny Care, Rob Buchanan, Jordan Turner-Hall and Seb Stegmann produced a bonus-point victory as Quins made a triumphant start to their Pool Three campaign after entering half-time locked at 13-13.
"This is the Heineken Cup and this is Biarritz. If you believe any team will just blast them away, it won't happen," O'Shea said.
"The players were so positive at half-time and that was good. We kept on trying to play and we knew the scores would come.
"I'm absolutely delighted with the response because last week against Exeter (43-28 defeat) we learned you have to work hard in every minute of every game."
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