The incident occurred at about 5pm local time yesterday in Peregrine Park in northern Sacramento.
Officer Doug Morse told the Sacramento Bee that attackers walked up and opened fire, then fled in a car.
A man aged in his 20s died at the scene. Police say he is believed to have been a gang member, but his name has not been released.
Mr Morse said six other people - including a seven-year-old - received non-life threatening injuries.
The group had gathered to celebrate a child's first birthday.
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