It was the first time in years that Francis, who turned 84 this month, has had to skip a papal event for health reasons.
A year-end vespers service that the pope was to lead on Thursday afternoon will be led by Cardinal Giovanni Battista Re, and the Friday Mass will be said by Cardinal Pietro Parolin, the Vatican Secretary of State.
The Vatican said the pope would lead his noon prayer on Friday as scheduled.
The pope suffers from sciatica, a condition that causes pain that radiates from the lower back along the sciatic nerve to the lower part of the body.
He can sometimes be seen walking with difficulty because of the pain and receives regular physical therapy because of the condition.