Shiels was carried off on a stretcher during his team's shock 2-1 home defeat by Annan in the Irn-Bru Third Division on Saturday and the club revealed they had received worrying news following a scan.
Rangers revealed that Shiels would head to England for expert opinion on the injury, which occurred during a challenge by Annan defender Steven Swinglehurst.
Manager Ally McCoist told the club's official website: "It's not great. He was in a lot of pain on Saturday night and he was heavily iced up but he was in pain again the next morning when I spoke to him.
"He went for a scan and the results are not great so he is heading down to London tomorrow to see a specialist. We will learn the next step after that but it's not looking too good.
"When I looked back at the incident with him if Dean had hit the ball first time it would have been better but hindsight is a wonderful thing.
"I am loathe to make any comment on the situation until we hear from the specialist."
David Templeton could replace Shiels in the team to face Elgin at Borough Briggs on Saturday.
McCoist said: "'Temps' is still struggling a little with an Achilles problem he picked up last Thursday but I'm still hopeful that he will be available for the weekend.
"We will give him every chance and we will need to wait and see."