Rivlin had written a Facebook post following Friday's arson attack on a Palestinian family's home in the West Bank village of Duma by suspected Jewish extremists.
The attack killed 18-month-old Ali Saad Dawabsha and left his parents and four-year-old brother critically wounded.
"More than shame, I feel pain," Rivlin wrote in Arabic and Hebrew. "The pain over the murder of a little baby. The pain over my people choosing the path of terrorism and losing their humanity.
Rivlin's post evoked a wave of more than 2,000 comments, some positive but others attacking him and recalling Israelis killed by Palestinians.
"Dirty traitor. Your end will be worse than (Ariel) Sharon's," said one comment quoted by the Maariv newspaper, referring to the late former Israeli premier who spent eight years in a coma.
Another said: "In Russia you would have been found by this point cut up inside a shoe box."
Israeli legal officials could not say whether incitement to violence was among the suspected crimes under investigation.
In 1995, then prime minister Yitzhak Rabin was gunned down at a peace rally in Tel Aviv by a Jewish extremist after a campaign of right-wing incitement against a peace deal with the Palestinians.
