The man, who the police only described as in his 70s, reportedly yelled "Heil Hitler" as he was led away handcuffed. But police investigators said it was too early to determine whether the attacks were a hate crime.
The shootings occurred about 1 p.m. Sunday in Overland Park, Kan. Two male victims were killed in the parking lot at the Jewish Community Center of Greater Kansas City, in Overland Park, and one female victim was killed a short time later in a parking lot at Village Shalom, a senior living community about a mile away, the police said.
The suspect was taken into custody a short time later at a local elementary school about a mile from Village Shalom, the police said.
At a news conference several hours after the shootings, the Overland Park police chief, John Douglass, said it was too early to determine if the shootings were hate crimes. He said only that the suspect was not a local resident and was not known to the police department before Sunday's attacks.
"Today is a very sad and tragic day," Douglass said at the news conference. "There are no words to express the senselessness of what happened this afternoon."
The attacks came on the eve of the Jewish holiday of Passover.
The shootings took place on a busy day at the Jewish community center as first round auditions were planned for a local singing competition called KC SuperStar. When the shooting was reported around 1 p.m., more than 100 people streamed into a hall inside the center, where they were held until it was safe to leave.
A high school student, Sophia Porter, arrived at the center for her singing audition only five minutes after the shooting. Porter, 17, said she saw police cars arriving before she was ushered into the lockdown area with dozens of adults and children.
"I was definitely shell-shocked when I heard what had happened," she said. "It was horrifying to think of the person who would be responsible for that, and my heart goes out to those affected."
The shootings stunned the close-knit Jewish community in the Kansas City area, just as they were preparing to celebrate Passover on Monday. The Jewish community center is the main hub for about 20,000 Jews in the Kansas City metro area, said Herbert Mandl, a retired rabbi and a local police chaplain.
"It's a very trying time for the community," he said. "We'll pull together. We'll survive."
The attacks started at a parking lot in the back of the sprawling Jewish community center near a theater, the police said. The suspect fired several shots and left. Several minutes later, an emergency call came from the retirement community reporting shots fired.
The authorities have not released the identities or ages of the three people who were killed.
Footage from local television stations showed a heavyset, bearded man wearing glasses being led away in handcuffs by police officers.
The back doors of the community center had substantial damage, the police said.
The Jewish Community Center released a statement Sunday evening saying the center would be closed Monday.
"Our hearts go out to the families who have suffered loss on this tragic day. Our heartfelt gratitude as well to all those in Kansas City and around the world who have expressed sympathy, concern and support."
Village Shalom said Sunday evening that it had very few details about what happened.
Mandl said he thought it was "suspicious" that both of the targets were places mostly used by the Jewish community, but said he understood that officials were being cautious in determining a motive.
At the news conference, when Douglass was asked by reporters whether the suspect yelled "Heil Hitler" as he was arrested, as some local media outlets reported, Douglass said it was too early to discuss what the suspect did or did not say.