The 121-times-capped goalkeeper was sent for tests after hurting the knee in training on Monday and is expected to sit out two to three days of this week's preparations in Malahide.
A spokesman for the Football Association of Ireland said: "Shay Given picked up a minor knee injury in training.
"After undergoing a scan, it was concluded that Shay should sit out training for the next 2-3 days for precautionary measures."
The Republic's Gannon Park training headquarters resembled a field hospital as Trapattoni's walking wounded were nursed back to health, with goalkeeper Given joining the likes of John O'Shea, Kevin Foley and Keith Fahey on the sidelines.
In addition, Keith Andrews, Shane Long and Jon Walters all sat out parts of the session. Only 12 men were actually on the training pitch as the first spell of the day drew to a close, although the 73-year-old Trapattoni later insisted those who rested had done so only as a precaution.
Given was sent for a scan on a knee injury he picked up in training on Monday, and a Football Association of Ireland spokesman confirmed: "After undergoing a scan, it was concluded that Shay should sit out training for the next two to three days for precautionary measures."
Trapattoni later suggested the 36-year-old Aston Villa keeper is his biggest concern ahead of Euro 2012 - which for the Republic kicks off against Croatia on June 10 - and hinted that either Sunderland's Keiren Westwood or David Forde of Millwall could play in Saturday's friendly against Bosnia.
He said: "There is only Shay Given, who has a little bit of a problem. We have to decide run the risk or stay. We have another two [keepers].
For this game, we will decide with the doctor because at this moment, we don't need to run the risk."
Sunderland defender O'Shea will almost certainly not play in the Bosnia game, with the FAI spokesman adding: "Giovanni Trapattoni has also decided that John O'Shea may not partake in Saturday's game against Bosnia for precautionary measures, but has confirmed that John will be fit in time for Euro 2012.
"John is undergoing rehabilitative treatment this week on his ankle."
However, Trapattoni was in relaxed mood as he ran through the catalogue of fitness concerns, with skipper Robbie Keane having finally joined up with the squad following his hamstring scare.
He said: "Robbie will be okay, but he has flown for too long and it was better he rested.
"O'Shea has assured me for the next game, he will be ready. He needs only a little bit. He has an ankle - not an injury, a knock - but he said, 'I will be ready for the game'."