Eliza Fletcher, 34, has still not been found, but Memphis police said they have evidence that leads them to believe she was seriously injured in the abduction near the University of Memphis campus.
Authorities said they have surveillance video of the abduction.
US marshals arrested 38-year-old Cleotha Abston on Saturday after police found his DNA on a pair of sandals discovered near where Ms Fletcher was last seen, according to the affidavit.
Police also linked the SUV vehicle involved in the case to a person living at a residence where Abston was staying.
Abston attempted to flee when US marshals arrived at that residence but was captured, according to the police affidavit.
Memphis police said on Sunday morning he was charged with especially aggravated kidnapping and tampering with evidence.
A second person was also arrested but apparently in connection with an unrelated offence, since police said they did not believe that person was connected to the abduction.
Authorities have said Ms Fletcher was out jogging at around 4am on Friday when a man approached her and forced her into an SUV after a brief struggle. Ms Fletcher was reported missing when she did not return home.
Police said a witness reported seeing Abston cleaning the inside of the SUV in question a few hours after the abduction and that he was “behaving oddly”.
Ms Fletcher is the granddaughter of the late Joseph Orgill III, a Memphis hardware businessman and philanthropist, according to news outlets.
Her family had offered a 50,000-dollar (£43,000) reward for information in the case.