The 7-foot, 6-inch former basketball player had neck fusion surgery following the accident and has spent the past eight weeks hospitalized and going through rehabilitation, according to the release.
"His very strong sense of faith is being tested as he participates in grueling physical therapy and learns how to cope with the challenges of paraplegia," the team said.
"Doctors have advised him that his road to recovery will be both long and arduous, perhaps an even more difficult physical challenge than playing professional basketball."
Still, he is in good spirits, according to the statement, and plans to use the accident "as a platform to bring greater public awareness to the importance of bicycle safety," the statement said.
Mavericks owner Mark Cuban said he was "saddened" to hear of the accident.
"Shawn has always been incredibly determined and shown a fighting spirit," Cuban said. "We wish him nothing but the best in his recovery. He will always be a part of our Mavs family."
In his more than eight seasons with the team, Bradley "demonstrated all of the qualities you want in a person representing your organization," Mavericks general manager Donnie Nelson said. "He has always exhibited unwavering grit and determination and we are thinking of him at this difficult time. He is a Maverick for life."