Both people were hospitalized in stable condition, police announced at 2:30 p.m. ET.
About 30 minutes later, police said they had ruled out a possible hate crime or religious motivation in the incident.
Police shut down the area surrounding the JCC at 6701 Hoover Road, but said there was "no ongoing threat."
"A perimeter has been set up nearby [and] residents can expect police activity in that area," the Indianapolis Metro Police Department tweeted.
"Drivers are asked to avoid the area."
Additional information about the suspect and victims was not immediately available.
The JCC is a 108-year-old community center. There is no requirement that its members belong to the Jewish faith.
The JCC did not immediately respond to calls seeking comment.
"Due to unforeseen circumstances theJCC is now closed," an automated response said.
Callers were instructed to monitor the JCC's website or call back later for updates.
Police said parents coming to pick up their children should use door 3 on the building's north side.
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