Police detained the teenager at an address in Kings Norton on Tuesday morning.
An investigation was launched after a man in his 60s was discovered with serious injuries in Chapel Walk on Friday, October 16. He remains in a critical but stable condition in hospital.
It is believed the man was robbed of his yellow Specialized Crosstrail Elite Disc 2016 model bike after being attacked by two people at around 1.50pm.
West Midlands Police are continuing to ask for anyone with information, or who saw anybody in the area with the yellow bike, to get in touch.
Detective Inspector Al Teague, from Force CID, said: "It's thanks to the response of the public we were able to identify and arrest a suspect this morning.
"This happened in broad daylight and we still need to hear from anyone with information who can help our enquiries.”
Anyone with information can contact officers by calling 101, and quoting log number 2383 of October 15.
Alternatively, contact Crimestoppers anonymously on 0800 555111 or at crimestoppers-uk.org