The payments are worth $US3,000 ($A4,612).
Moldovan officials have regularly accused Moscow of meddling in their domestic politics by stoking pro-Russian sentiments in a subversive campaign to topple the government as it bolsters ties with the West, accusations Moscow denies.
Shor, under Western sanctions for efforts to destabilise Moldova on Russia's behalf, said he would make daily payments to each protester totalling a monthly $US3,000 ($A4,612) if they began protesting in the capital Chisinau starting on Saturday.
"Yes, I am...compensating you in such a way that already from Saturday you'll feel the effects of the victory that we will soon achieve," he said in a video posted to social media.
He added that accounts for payment would be opened up directly at the protest site.
Moldova's National Police said in a statement that Shor's message was "criminal incitement" and warned Moldovans they risked investigation if they engaged with the offer.
"Law enforcement will not allow criminal groups to organise illegal protests aimed at causing disorder and violence. Any attempt will be firmly rejected within the legal framework," the police statement said.
Moldova says Shor, who was convicted of helping steal $US1 billion ($A1.5 billion) from the country's banking system in 2014, is Moscow's primary agent of influence.
Officials have barred his party from standing in elections and banned media assets linked to him.
Earlier this month, a Moldovan court jailed a pro-Kremlin regional leader for channelling money from Russia between 2019 and 2022 to finance Shor's party.
A small former Soviet republic situated between Ukraine and EU and NATO member Romania, Moldova will hold parliamentary elections on September 28.
The ruling party is aiming to hold on to its majority to keep the country's pro-European trajectory intact.
