On July 26, Ukrainian President Petro Poroshenko revoked Saakashvili's Ukrainian citizenship over the later's allegedly submitting false information while applying for a passport.
Thousands of his supporters had gathered on the Ukrainian side of the border and some pushed through guards and brought Saakashvili into Ukraine at the Medyka-Shehnyi crossing - 80 kilometers (50 milies) west of the Ukrainian city of Lviv.
While in Warsaw on Friday, Saakashvili asserted that Ukraine was witnessing a roll-back of reforms and efforts to stem corruption, reiterating that he wanted to get back into politics.
The criminal case was opened on charges of "illegal smuggling of people across the state border of Ukraine", said a statement on the website of the National Police. "We should have democracy in our country and should not have the diktat of the oligarchs". He forfeited his Georgian citizenship when he accepted Poroshenko's welcome to Ukraine and the post as Odessa governor two years ago. He gave up his Georgian citizenship when he got the job in Ukraine. The announcement said that "in accordance with Ukraine's legislation, the train will move on as soon as that person leaves the train".
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Interior Minister Arsen Avakov called the border breach "an attack on the state's basic institutions".
Saakashvili, a former president of Georgia, is campaigning on a strong anti-corruption platform.
He left in disgrace for Ukraine in 2015 to work for the country's pro-Western authorities as governor of the key Odessa region on the Black Sea. Saakashvili was outside the country when the decision was made.
As of this May, the approval rating of Mr Saakashvili's party, the Movement of New Forces, stood at 1.1 per cent, according to a local pollster.
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Saakashvili and a crowd of supporters are proceeding into Ukraine on foot after breaking through a line of guards on the Polish-Ukrainian border. Ukrainian Member of Parliament Ivan Krulko, cited by BBC, said the guards had allowed Saakashvili into the country. But while perhaps not a threat as a direct rival, Saakashvili could prove to be an effective weapon against Poroshenko for powerful opposition figures like Yulia Tymoshenko, who was with him at the border on Sunday.
"I was tremendously impressed", he said.
The Ukrainian president praised on Monday the correct actions of domestic border guards during Mikheil Saakashvili's breakthrough of the state Ukrainian border.
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