Squire left the field about 25 minutes into Friday night's game against the Blues with what was initially thought to be a cut lip.
But he was found to be coughing up blood and was sent to hospital on Friday night.
He was assessed at hospital and found to be fine and returned to Dunedin with the team on Saturday morning.
Tanaka injured his calf muscle at the captain's run in Auckland on Thursday.
It did not come right and he was a late withdrawal from the side for the game at Eden Park.
He was replaced by Josh Renton who did not get on the paddock.
Tanaka will be monitored over the next few days to see whether he is available for the first home game of the season against the Hurricanes on Saturday night.
Lock Joe Wheeler and prop Daniel Lienert-Brown were also forced off for a period in the match on Friday night due to suspected concussion.
An independent match medical officer has been appointed to each game.
This was introduced last year but is expected to be more prominent this season as the concussion issue comes under the spotlight.
The official watches the game on a television monitor on the sideline and, if he spots a player he suspects has been concussed, the official has the ability to take the player off the field for evaluation and to undergo a concussion test.
Wheeler was slightly dazed when in a collision in the first half but it was more of a sore shoulder than a head knock which had him struggling immediately after the incident.
There were no other significant injuries for the Highlanders but it was not a happy trip to Auckland.
The side lost, the bus from the airport broke down when they arrived on Thursday and the bus did not even turn up on Saturday morning to take them from the hotel to the airport, forcing the players to take taxis.
