The Twitter user, who was not named, was alleged to have referred to men who support women driving as "cuckolds who should be killed," according to state-linked Asharq al-Awsat newspaper.
The prosecutor's announcement comes two days after a separate arrest warrant was issued for a man who threatened in a video clip posted online to attack women drivers.
Many Saudis welcomed Tuesday's announcement by King Salman lifting the ban by next year, but others expressed opposition online or in quiet conversations after decades of support for the policy by prominent clerics.
In the statement, the prosecutor vowed to monitor for threats of abuse and pursue cases against those who "incite attacks against society and violations of the rights of others".
(Reporting by Katie Paul; Editing by Stephen Powell)
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