Hatice Cengiz wrote an open letter to the singer published on Saturday in the Washington Post in which she urged Bieber to cancel the performance to "send a powerful message to the world that your name and talent will not be used to restore the reputation of a regime that kills its critics."
President Joe Biden's administration released a US intelligence report in February implicating Saudi Arabian Crown Prince Mohammed bin Salman in Khashoggi's 2018 murder in Istanbul but spared him any direct punishment. The crown prince denies any involvement.
"Do not sing for the murderers of my beloved Jamal," Cengiz wrote. "Please speak out and condemn his killer, Mohammed bin Salman. Your voice will be heard by millions."
Bieber, who is Canadian, is among a group of artists scheduled to perform as Saudi Arabia hosts the Formula One Saudi Arabian Grand Prix in Jeddah.
"If you refuse to be a pawn of MBS, your message will be loud and clear: I do not perform for dictators. I choose justice and freedom over money," Cengiz wrote, using the crown prince's initials.
Human rights groups have urged the performers to speak out against human rights issues in the kingdom.
"Saudi Arabia has a history of using celebrities and major international events to deflect scrutiny from its pervasive abuses," Human Rights Watch said on Wednesday.
The advocacy group urged the performers, who also include rapper A$AP Rocky, DJs David Guetta and Tiesto and singer Jason Derulo, "to speak out publicly on rights issues or, when reputation-laundering is the primary purpose, not participate."
Khashoggi, a Saudi-born US president who wrote opinion columns for the Washington Post critical of the Saudi crown prince, was killed and dismembered by a team of operatives linked to the prince in the kingdom's consulate in Istanbul.