Police arrested 38-year-old Alejandro Benitez, of San Jose, on Friday in connection with an incident in which police and firefighters responded to reports of an infant in distress in the 2100 block of Mendota Way around 2:20 p.m. on April 4.
The boy was unresponsive when they arrived, and later died at Regional Medical Center of San Jose.
Police said Benitez was the boyfriend of the child's babysitter, who was taking care of him at her Mendota Way home.
The case was not initially considered a homicide, but its reclassification as a murder has pushed San Jose's homicide total to 32 this year.
The killings have motivated Assemblywoman Nora Campos, D-San Jose, a former San Jose city councilwoman, to call on Police Chief Chris Moore to request that the California Highway Patrol step in to help local police get the violence under control.
On Tuesday night, a man in his 20s was stabbed to death inside a Safeway supermarket at 3002 Story Road, police said.
It was the city's eighth killing since the beginning of the August. At this time last year, there had been 27 homicides. Thirty-nine people were murdered in 2011, which was nearly double the 20 homicides in 2010.
"I think when you look at the increase in gang violence, and the increase in homicide rates, what you see is a crime wave sweeping across the city of San Jose," said John Robb, vice president of the San Jose Police Officers' Association.
Robb said part of the problem is that San Jose has fewer officers per capita than most major cities in the country, and is having trouble retaining its officers because of pay cuts.
"We have officers resigning at a record rate," Robb said.
He said about 100 have resigned in the past 18 months alone.
In a city with an understaffed police force, Robb said, "Criminals are going to commit more crimes."