Bernalillo County Sheriff's officials said Xavier Macafee, 29, was being held on suspicion of burglary.
Macafee, of Albuquerque, was booked into jail last Friday and made his initial court appearance Monday, according to authorities who didn't immediately know if he had a lawyer.
Deputy Aaron Williamson, a spokesman for the sheriff's department, said none of the stolen items have been recovered but detectives were investigating the case.
He said other items reported taken from Cranston's car were an iPad, a shoulder bag and "miscellaneous personal items."
Cranston's car was broken into Dec. 20 while it was parked at Sandia Peak, authorities said.
The award-winning AMC TV series is set in Albuquerque and is filming its fifth and final season in and around the city.
"Breaking Bad" follows Cranston's character Walter White producing and selling methamphetamine with a former student named Jesse Pinkman, who's played by Aaron Paul.
A call to AMC network officials in California for comment on the script theft wasn't immediately returned Monday afternoon.