"This will not only bring the justice we have been seeking.... but it could also prevent similar acts recurring," Hatice Cengiz said in a statement.
It comes after a US intelligence report found that Crown Prince Mohammed bin Salman had approved Khashoggi's murder.
Saudi Arabia has rejected the report.
Crown Prince Mohammed, who is effectively the kingdom's ruler, has denied any role in the murder.
Khashoggi was killed while visiting the Saudi consulate in Istanbul, Turkey, in October 2018 and his body was dismembered.
The 59-year-old journalist had once been an adviser to the Saudi government and close to the royal family, but he fell out of favour and went into self-imposed exile in the US in 2017.
From there, he wrote a monthly column in the Washington Post in which he criticised the policies of Prince Mohammed.
In his first column for the newspaper, Khashoggi said he feared being arrested in an apparent crackdown on dissent overseen by the prince.
"It is essential that the crown prince, who ordered the brutal murder of a blameless and innocent person, should be punished without delay," Ms Cengiz said on Monday.
"If the crown prince is not punished, it will forever... endanger us all and be a stain on our humanity," she added.
Ms Cengiz, a Turkish academic researcher, made a plea that world leaders distance themselves from the crown prince and impose punishments such as sanctions on Saudi Arabia.
"Starting with the Biden Administration, it is vital for all world leaders to ask themselves if they are prepared to shake hands with [Prince Mohammed]," she said.
"I urge everyone to put their hands on their hearts and campaign to punish the crown prince," Ms Cengiz added.
