Gary Lee Bullock, 43, of Redway was taken into custody by Humboldt County deputies in the killing of the Rev. Eric Freed, according to a statement released by Eureka police.
Bullock had been named in an arrest warrant. The statement says he had been in and out of police custody in the hours before Freed died.
Officials were seeking a motive in the killing.
Freed's body was found on New Year's Day in the St. Bernard Church rectory after he failed to show up for morning Mass.
Bullock was initially arrested on Tuesday for public intoxication in Garberville and taken to jail in Eureka, His erratic behavior led police to send him to a hospital for an evaluation.
He became agitated and deputies had to restrain him. He was booked into jail for about eight hours then released shortly after midnight.
At 2:00 a.m. Wednesday, Eureka police responded to a call about a suspicious person a couple blocks from the jail and a short distance from the church where Freed was found.
Officers referred Bullock to an emergency shelter for the night. Later that evening, a security guard heard noise near the church and went to investigate. He saw a man matching Bullock's description and, after a short conversation, told him to leave the property, police said.
It is not clear exactly when Freed was killed An autopsy is scheduled for Saturday.
Investigators found signs of forced entry and a struggle at the church. Police are searching for Freed's missing 2010 Nissan hybrid.
"The reverend was a victim of a violent crime," Eureka police Chief Andrew Mills said. "We're not sure on the motive but don't believe it was a robbery at this point."
Freed had taught classes on religion at Humboldt State University since 2007, including "Introduction to Christianity" and a class on Japanese calligraphy. Humboldt State is a small university of 8,000 students near Redwood National Park, on the edge of the Pacific Ocean.
Colleague William Herbrechtsmeier described his friend as a man of keen intellect who had a robust laugh and wide-ranging interests, including sports.
"It's just horrid that someone of his quality would be snuffed out in this way," he said.
Freed grew up in Southern California and graduated from Loyola Marymount University. He completed his graduate studies in linguistics while in Italy, where he also learned how to speak Italian.
Freed also worked on a book related to the bombing of Hiroshima, helping a survivor translate haikus about the experience and providing commentary. When the book was published a few years ago, Humboldt State held a conference on genocide and violence.
Humboldt is a diverse community known for dairy farming, fishing, a declining logging industry and marijuana and methamphetamine production.