Kanter, 24, took screenshots of the threats, which are written in Turkish.
"Death threats continue to fall," Kanter posted on Twitter, in Turkish. "Prayer does not stand still."
On Friday, a military faction launched a failed coup attempt to overthrow Turkish president Tayyip Erdogan's regime.
After a terrorist bombing in Turkey's capital of Ankara in March, Kanter was outspoken against Erdogan's government. The attack killed 37 people and injured more than 100. Kanter criticized the blocked access to social media and the limited broadcast media coverage.
In June 2015, Kanter said he was left off Turkey's national team for Eurobasket 2015 because of his politics. National team coach Ergin Ataman said at the time that the decision was not political.