Skipper and star midfielder O'Driscoll dislocated his left shoulder during the first 90 seconds. The Irishman was carried off on a stretcher and taken to hospital, but the Lions management are now awaiting tapes of the incident to assess exactly how it happened.
The Lions never recovered from his departure as they crashed to defeat.
"Brian is not good. It is a very bad dislocation, and it took 25 minutes to get his shoulder back in," said Lions head coach Sir Clive Woodward.
"I don't think a lot of the team saw it - it was off the ball. The pictures won't lie so we have just got to see what happened."
Hill's condition is currently being assessed by the Lions medical staff, with a further update likely later.
Woodward added: "It has been a bad day. Richard Hill has got a serious knee problem, and Tom Shanklin is out of the trip on medical advice."
Woodward has yet to decide on any replacements for the latest injured players, and no decision will be made on O'Driscoll's replacement as captain until the selection is decided for next Saturday's second Test in Wellington.