Saakashvili was in the United States when news of the loss of his Ukrainian citizenship broke, he said on Facebook.
He accused President Poroshenko of Ukraine of crossing a red line.
"I have only one citizenship, that of Ukraine", Saakashvili said in the Facebook post.
"This is the stupidest thing that could have been thought up - a sign of weakness that reflects badly on the president of Ukraine", he said in a post on Facebook that was shared by Saakashvili.
Saakashvili was forced to leave the position of Odessa governor in November a year ago after spoiling relations with the Ukrainian authorities, which he vigorously supporting during the 2014 coup.
Saakashvili resigned last November, citing opposition to reform, and set up a new political party.
Saakashvili, 49, is an adamantly pro-Western reformist who was swept to power in Georgia by the peaceful Rose Revolution protests of 2003 and served two terms as president in 2004-2013.
Georgia's leadership has not yet commented publicly on Poroshenko's decision.
It did not provide the exact reason, but stated that this could be done if a Ukrainian national acquired citizenship of another country or submitted false documents. He further said the extradition of Saakashvili, who faces several charges in Georgia, depends on the request from Georgia's Government.
In December 2015, Georgian authorities stripped Saakashvili of Georgian citizenship as dual citizenship is not allowed in Georgia.
"Every day that I have had a Ukrainian.passport I have worked so that Ukraine could win and become a real European country", he said.
Ukraine's State Migration Service announced on Wednesday that Ukrainian President Petro Poroshenko had issued a decree rescinding the citizenship of Georgian-born Saakashvili while he was in the United States.
"Their secret meeting lasted more than two hours and was nearly entirely devoted to me", Saakashvili claimed.