Elkus is suspected of killing Dr. Ronald Franklin Gilbert, 52, of Huntington Beach at the medical office in Orange County.
Police said they found Elkus and Gilbert in a second-floor room after several 911 callers reported six or seven shots fired. A gun was found at the scene.
The doctor had been shot several times in the upper body and was declared dead at the scene in Newport Beach.
Elkus had been undergoing treatment for prostate problems, neighbors told the Los Angeles Times. He frequently visited Gilbert, neighbor James Lord said.
The Orange County sheriff's jail website listed Elkus as a barber, but neighbors said he was retired.
An autopsy was planned Tuesday and Elkus was scheduled to appear Wednesday in court. Police searched his home but declined to disclose what they found.
Gilbert, a married father of two children, appeared to be the only target of the attack, police spokeswoman Kathy Lowe said.
Dr. Jeffrey Lauber, a dermatologist, said he frequently referred patients with cancer symptoms to Gilbert.
"He's the best there is," Lauber said. "Not only is he a very good urologist, he's a pillar of the community."
Lauber couldn't imagine why anyone would want to shoot Gilbert.
"This doesn't happen down here," he said of the wealthy enclave 45 miles southeast of Los Angeles.
Gilbert dealt with general urology, sexual dysfunction and related surgical techniques including vasectomies, bladder and prostate cancer, according to his biography on the website of the Orange Coast Urology Group, which he joined in 1993.
One of his specialties involved using a laser to vaporize prostate tissue blocking the urinary tract. His biography called him a "people person" and said he enjoys helping people.
He decided to become a doctor mainly because his father is a doctor, the biography said, adding that Gilbert had been a stockbroker and a singer in a rock band.