Masked officers dragged Mr Saakashvili from his home while supporters protested in the street.
Two hours after Mr Saakashvili entered the van, it was still at a standstill as the crowd chanted "Kiev, rise up!"
Saakashvili was a key figure in the 2003 Rose Revolution protests in Georgia that ousted the country's president.
His stand-off with Mr Poroshenko ignited long-simmering popular discontent with the slow pace of the president's much-promised reforms.
Saakashvili issued the call for an encampment at Kiev's Independence Square during a rally that news reports said attracted 2,500 people.
As protesters blocked the police van carrying Mr Saakashvili, who left Georgia in 2013 and served as governor of Ukraine's Odessa region in 2015-16, the authorities accused the firebrand politician of working to overthrow the government. But he quit that office in 2016, complaining that his efforts to root out corruption suffered official obstruction. He then served as president for almost a decade.
Mr Saakashvili, formerly Georgian, then Ukrainian, is now a stateless person, as his Ukrainian citizenship was removed by Mr Poroshenko, after a falling out. Saakashvili forced his way across Ukraine's border with Poland earlier this year, with help from protesters.
The Security Service said in a statement that Saakashvili is facing a criminal investigation for "assisting members of criminal organizations or hiding their criminal activities".
Ukrainian Prosecutor General Yuriy Lutsenko has said that Mikheil Saakashvili, the leader of the Movement of New Forces party, has received half a million US dollars from Ukrainian businessman Serhiy Kurchenko in order to organize protest rallies.
Saakashvili spearheaded several protests in Kiev, but they typically drew fewer than 4,000 people.
"All the rallies were financed by foreign oligarchs that aimed to seize power by illegal means", Lutsenko said.