This is the highest recognition that Mexico gives to a foreigner, according to the paper.
Others who have received the award include Walt Disney, former Cuban President Fidel Castro, former Sen. Ted Kennedy, Bill and Melinda Gates and former Argentine first lady Eva Peron.
Kushner and Ivanka and Vice President Mike Pence will represent the US at his inauguration.
Speaking Tuesday at an unrelated event, outgoing Nieto called Kushner a "grand ally of Mexico" and an important player in maintaining a good relationship between his country and the Trump administration.
According to NPR, the award choice has shocked many in Mexico, however, where President Trump is not well-liked.