Cine will remain in the United Kingdom until doctors determine it is safe for him to fly back to Minnesota.
O'Connell choked back tears in announcing the details of Cine's injury, which occurred with 1:08 remaining in the first quarter of the Vikings' 28-25 victory.
While he was blocking on a punt return, Cine's leg bent unnaturally on the Tottenham Hotspur Stadium playing surface,
which is transitioned from grass to artificial turf for NFL games.
Cine was immediately fitted with an air cast and taken off the field on a cart.
"Very tough moment for our team," O'Connell said. "[Cine is] obviously a guy that, from Day 1, has been a personal favorite of mine and does everything we've asked.
He was continuing to progress in his rookie year and really had a dynamic role for us on special teams."
Cine, the Vikings' first-round pick in this year's draft, was slowed during training camp and early this season by a knee injury.
He had played only two snaps on defense in addition to his special-teams role.