Paramedics were called to the scene and took Boyle away voluntarily, the report says.
"It was all done very calmly. They didn't want to stress or upset her. She didn't look well - she looked lost, not all there," a source told the paper.
A spokesperson for the talent competition responded to the claims with a statement:
"Following Saturday's show, Susan is exhausted and emotionally drained. She has been seen by her private GP, who supports her decision to take a few days out for rest and recovery. We offer her our ongoing support and wish her a speedy recovery."
Boyle is 48, native to Blackburn, West Lothian. She came in second place in the competition, beat by dance troupe Diversity.