The court, as in many recent controversial rulings, divided 5-4. Kennedy, widely seen as the swing vote, wrote the majority opinion striking down a Florida law.
Florida and some other states had adopted the standard of an IQ of 70 measured by standard intelligence tests after the high court ruled 6-3 in 2002 that putting those with intellectual disabilities to death is unconstitutional.
"Intellectual disability is a condition, not a number," Kennedy wrote. "In using these scores to assess a defendant's eligibility for the death penalty, a State must afford these test scores the same studied skepticism that those who design and use the tests do, and understand that an IQ test score represents a range rather than a fixed number."
Justice Samuel Alito, writing for the minority, said that Kennedy was not giving enough recognition to the powers of state legislatures. He also suggested that inmates facing execution are tested many times, reducing the margin of error.
"The Court's approach in this case marks a new and most unwise turn in our Eighth Amendment case law," Alito wrote. "Under our modern Eighth Amendment cases, what counts are our society's standards --which is to say, the standards of the American people -- not the standards of professional associations, which at best represent the views of a small professional elite."
The Florida law was challenged on behalf of Freddie Lee Hall, who was sentenced to death for killing a young pregnant woman in 1978. Hall tested at between 60 and 80, but the lower scores were dismissed.
In mid-May, a federal appeals court granted a stay to Robert James Campbell, hours before he was to be executed in Texas for raping and killing a young bank teller. Campbell's lawyers argued that Texas officials concealed test results that showed he is intellectually disabled.