Sheriff's deputies arrested the boy Friday around 5 p.m., according to Lt. Rick Sung.
The high school, located at 21840 McClellan Road, canceled classes on Thursday following the bomb threat, Sung said.
Santa Clara County authorities received a report from San Jose police at 6:39 a.m. of the threat, Sung said.
Police reported that graffiti at Lynbrook High School, located at 1280 Johnson Ave. in San Jose, referenced a bomb threat at Monta Vista High School, Sung said.
A specific male teacher, whose name hasn't been released, was referenced in the threat, he said.
Sheriff's deputies and bomb-detecting dogs searched the area and found no explosive devices, Sung said.
Because of its close proximity to Monta Vista High, Lincoln Elementary School, at 21710 McClellan Road, was also closed on Thursday, Sung said.
"Sheriff's deputies worked relentlessly for almost two days until the arrest of the juvenile who is responsible for the crimes," Sung said. "Overall, there was great communication and cooperation between the Sheriff's Office and the Monta Vista High School administration."
Classes at Monta Vista resumed Friday morning.