Closed circuit TV footage showed the male runner knocking a 33-year-old woman head-first in front of a bus, which just managed to swerve out of her way.
"Police investigating an assault after a jogger appeared to push a woman into the path of an oncoming bus in Putney have made an arrest," London police said in a statement.
The man is being held on suspicion of causing grievous bodily harm after an arrest in the nearby Chelsea area of London, police said. The victim received minor injuries from the incident.
The arrest came after a public appeal earlier the week for help in tracing the jogger. Although the incident happened in May, police said they had received a "good response" from the appeal, and said they were still looking for other witnesses.