A call to police led authorities to a home and a standoff with the man, who was eventually taken into custody, East Cleveland Mayor Gary Norton said.
Michael Madison, 35, was charged with three counts each of aggravated murder and kidnapping. He didn't enter a plea at a brief court appearance Monday where bail was set at $6 million. He also waived his right to a preliminary hearing.
Police and volunteers scoured about 40 empty homes Sunday until their search was suspended, with no immediate plans to resume.
Authorities said they had identified only one of the victims, Angela Deskins, who was believed to be 38 years old. The other two bodies were too badly decomposed to identify. The medical examiner also said he couldn't determine a cause of death because of the bodies' conditions.
The mayor has said the suspect indicated he might have been influenced by the earlier case of a Cleveland serial killer convicted in the deaths of 11 women.
The first body was found in a garage Friday. Two others were found Saturday - one in a backyard and the other in the basement of a vacant house. The bodies, all women, were found about 100 to 200 yards apart, and authorities say the victims were killed in the previous six to 10 days.
Each body was wrapped in a plastic bag in the fetal position. "It didn't look like a person could actually fit in the bag," said East Cleveland Police Chief Ralph Spotts.
Police and volunteers scoured about 40 empty homes Sunday for more evidence until their search was suspended, with no immediate plans to resume, Spotts said. Norton said Monday that no bodies were found, but Spotts stressed that the investigation remained open.
It's the third recent high-profile case in the Cleveland area that involves missing women.
In May, three women who separately vanished about a decade ago were found captive in a run-down house. Ariel Castro, a former school bus driver, has been charged with nearly 1,000 counts of kidnap, rape and other crimes and has pleaded not guilty.
Castro is accused of repeatedly restraining the women, sometimes chaining them to a pole in a basement, to a bedroom heater or inside a van. The charges say one of the women tried to escape and he assaulted her with a vacuum cord around her neck. He also fathered a daughter with one captive, authorities said.
In 2009, Anthony Sowell was arrested after a woman escaped from his house and said she had been raped there. Police found the mostly nude bodies of 11 women throughout the home.
Sowell's victims ranged in age from 24 to 52, all were recovering or current drug addicts and most died of strangulation; some had been decapitated, and others were so badly decomposed that coroners couldn't say with certainty how they died.
He was found guilty in 2011 and sentenced to death.