The weapon was found by police searching a car park in Chicago near where an abandoned car was found with the body of seven-year-old Julian King inside.
It is being put through forensic tests, but it is believed that the ammunition from the recovered gun is the same make as the shell casings found at the murder scene.
Police were unable to give out details other than that a few other "small bits of evidence" were found in the bushes in the car park around the corner from where the car was found.
Hudson's mother, 57-year-old Darnell Donerson, and brother, 29-year-old Jason Hudson, were found on Friday shot dead in their home on Chicago's South Side. Her nephew Julian was missing, and on Sunday the Dreamgirls actress offered a $100,000 (£60,000) reward for his safe return.
But his body was discovered on Monday in an white Chevrolet Suburban in Chicago's West Side. He had also been shot.
Meanwhile, the convicted criminal suspected of the murders told police he is innocent but refused to take a lie-detector test, a police source said.
William Balfour, the 27-year-old stepfather of Hudson's nephew and estranged husband of her sister, told detectives he had a good relationship with the Hudson family, the police official said. When detectives asked Balfour to take the polygraph test, he stopped cooperating and refused to take the test.
Balfour has not been charged, but he is being held in custody for parole violation. Police think he may have had an accomplice, but he is the only suspect in the killings themselves.
His mother, Michele Balfour, has said Hudson's mother threw Balfour out of the family home last winter. She denied her son had anything to do with the killings.
He served seven years in prison for an attempted murder and vehicle hijacking in 1999.
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