Captain Adam Khamkhoyev, 30, a paratrooper commander, was buried in his native Ingushetia in Russia.
Khamkhoyev, a graduate of the elite Ryazan Airborne Forces school, was the commander of a Russian airborne assault squadron and the son of Yevkurov’s sister.
He was reportedly killed on the night of Friday into Saturday 20 to 21 May.
Baza news outlet said: “Yevkurov shared his condolences, spoke to the elderlies and the religious part of the community, and then flew back to Moscow.
“The funeral of Captain Adam Khamkhoyev, graduate of elite Ryazan Airborne Forces school was held on Sunday, 22 May, in Karabulak, Ingushetia.”
The commander’s body was returned home immediately, in contrast to the wait of weeks or months faced by other grieving relatives.
The case is the first when such a senior Putin official has suffered the loss of a close relative in his war in Ukraine.
Yevkurov - himself a career soldier and decorated paratrooper who won the Hero of Russia honour, the country’s highest award - has not commented on his nephew’s death.
Russia has not given details of where or how he died.
Yevkurov is a former governor or Ingushetia, and is now one of the deputies to close Putin ally Sergei Shoigu, the Russian defence minister.
He was the subject of an assassination bid in 2009.
In March he was captured in a video visiting a bed bound soldier in hospital.
The serviceman had lost a leg and looked wide-eyed and scared as Yevkurov told him: “ I hope you’ll get back on your feet.”