The Canadian singer is among the stars set to perform at the kingdom's first Formula One Grand Prix in Jeddah.
But Hatice Cengiz wrote an open letter to Bieber urging him to "send a powerful message" by pulling out.
Khashoggi, a prominent critic of the Saudi regime, was murdered at its consulate in Istanbul in October 2018.
He had gone there to pick up documents for the couple's wedding. The journalist's body was dismembered as Ms Cengiz waited outside.