Strokosch was forced off just 13 minutes into Scotland's 38-18 Calcutta Cup defeat to England at Twickenham on Saturday.
Scotland team doctor James Robson said: "It would seem he has a fractured orbit (area around the eye) but, as ever with such collision-type injuries, they can take time to settle.
"He will be examined by Mr Martin Paley, a maxillary facial specialist at Spire Murrayfield Hospital on Tuesday, to determine the extent of the injury and any recovery schedule."
Dougie Hall (knee), David Denton (knee) and Johnnie Beattie (ankle) will all require medical attention over the next few days.
The Scotland squad reassemble in Edinburgh on Sunday night to begin preparations for next weekend's game against Italy at Murrayfield.
Among them will be Glasgow centre Peter Horne, who missed the England game due to a thumb injury.
Interim coach Scott Johnson has called up eight players from the Scotland A squad that beat England Saxons 13-9 last Friday - props Jon Welsh and Alasdair Dickinson, hooker Steve Lawrie, loose forward Richie Vernon, scrum-half Sean Kennedy, fly-half Tom Heathcote and wings Nikki Walker and Duncan Taylor.
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