The segment will include footage of the pair recording jazz track Body and Soul at the Abbey Road Studios in March.
"It was a thrill to record with Amy," said Bennett, who called the song "a testament to her artistic genius".
"Our family is honoured that the VMAs are giving Amy this wonderful tribute," said Mitch Winehouse, Amy's father.
Columbia Records are to release Body and Soul as a charity single in support of a foundation established by the late singer's family.
The track - the last Winehouse recorded prior to the death - will also feature on Bennett's Duets II album, which is being released on 20 September.
Lady Gaga, Adele and Bruno Mars are among other artists who will appear at this year's awards, to be held at the Nokia Theatre in Los Angeles on Sunday.
Winehouse was found dead at her London home on 23 July. The singer, famous for such hit songs as Back to Black and Rehab, was 27.
According to her family, toxicology results have revealed there were no illegal substances in the singer's system before she died.
An inquest on 26 October will determine the exact cause of Winehouse's death.