Marshall Grant Neely III, 58, of Franklin, Tennessee, was arrested after the crash, which occurred on Saturday, according to police, and faces several charges, including reckless endangerment, leaving the scene of an accident, failure to immediately notify of an accident and failure to render aid.
Neely was booked into the Williamson County Detention Center in Tennessee, and officials said that he may face additional charges, possibly including federal ones, in the days ahead.
He was released on $11,500 bond and has a court date scheduled for July 20. Calls to Neely from ABC News on Sunday afternoon were not immediately returned.
Officials said the cyclist, Tyler Noe, sustained serious but not life-threatening injuries and is recovering at a local hospital.
The NPS said Noe was biking with another man, Greg Goodman, when Neely's black Volvo clipped Noe, knocking him to the ground.
Goodman was using his GoPro and posted a video of the crash on social media.
Neely is an employee of the University School of Nashville and was listed as a dean of students as of Saturday night. As of Sunday morning, however, his information was no longer listed with the school.
The school released a statement on Sunday afternoon, saying, "Marshall Neely served as dean of students at University School of Nashville before transitioning to a part-time role this summer. He also is parent of two alumni. As of today, USN has placed Mr. Neely on leave of absence while we investigate the circumstances."