The Right Reverend Vincent Logan said he had reluctantly made the decision after advice from doctors.
The bishop was due to attend the Holyrood reception with the Queen and an outdoor Mass in Glasgow during Pope Benedict XVI's visit in two weeks.
A spokeswoman said he had broken his shoulder in a fall at his home.
'Deeply sorry'She added that Bishop Logan was very disappointed not to be taking part in the events after the "most unfortunate accident".
The Pope will be in the UK from 16 to 19 September, in what will be the first papal visit to the UK since John Paul II in 1982.
Pope Benedict will start his tour in Edinburgh, where he will be welcomed by a special St Ninian's Day parade.
Bishop Logan said: "I am deeply sorry to have to make this announcement, but I have to adhere to the medical advice I have been given.
"I am so sorry to be unable to participate in the meeting of the Holy Father with Her Majesty the Queen at Holyrood and to concelebrate with the Holy Father, my brother bishops, and fellow priests at Bellahouston and at various events in England.
"I will most certainly join in prayer with everyone, at every event, throughout the four days Pope Benedict is with us, and I feel sure that all of us will be enriched and encouraged by his presence among us."
SIC: BBC/UK