The American Jewish Committee said the attack was not an isolated incident and called on senators to broaden hate legislation to include protection for houses of worship.
Mr Pence tweeted he was "Sickened and appalled by the cowardly act of vandalism at Congregation Shaarey Tefilla; a beautiful synagogue in Carmel, Indiana where I have many good friends."
He added: "Those responsible must be held accountable. These vile acts of anti-Semitism must end."
A statement by the Indiana Jewish Community Relations Council said an investigation was underway.
According to a 2017 study there were around 17,900 living in Indiana, one of the smaller populations in the United States.
