The incident took place in Lindelof's home city of Vasteras, which is west of the Swedish capital of Stockholm.
Manchester United confirmed Aftonbladet's story when asked for comment.
A police statement said a man in his 30s riding a bicycle snatched a bag belonging to a woman in her 90s on Monday morning.
"A man who was in the vicinity is said to have run after the suspected perpetrator, caught up with him and held him until the police arrived at the scene," police said, without naming Lindelof.
"The police want to take the opportunity and thank the witness for a quick and wise intervention."
The arrested man faces charges of aggravated theft and minor drug offenses.
Information from the Associated Press was used in this story.