The 19-year-old girl abused the man and spat on him before walking off. The attack, apparently unprovoked, occurred near a bus station in Coventry's Trinity Street at 8.30pm on August 10.
Police acted after a video of the incident, recorded by a passer-by on a mobile phone, went viral online and was shared on Facebook.
The girl was arrested yesterday, with police saying she would be questioned about the attack. Police are treating the attack as "serious malicious wounding", which is punishable with up to five years in prison.
The video of the attack triggered a wave of revulsion after it was circulated widely on social media, The Coventry Telegraph reported.
Coventry police chief Andy Nicholson was quoted by the paper as saying: "This was a despicable, violent attack on an elderly man in broad daylight. The victim is an 80-year-old man, he was left with a bloodied nose and a black eye.
"A video showing the assault spread rapidly on social media and quite rightly, the offender's actions are being condemned by everyone who's viewed it." Police are keen to hear from people who witnessed the attack and moments leading up to it, and have urged persons who shared the video or still images of the assault to remove them from social media accounts as they could hinder the inquiry.