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.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.