The resignation comes two days after demonstrations against the pact in central Brussels descended into scuffles, with police forced to use tear gas and water cannon to restore order.
After a debate in parliament where opposition parties refused to lend their support to allow his government to keep working until legislative elections in May next year, Michel announced he would quit.
"I have taken the decision to submit my resignation and it is my intention to go to see the king immediately," Michel said.
The Flemish nationalist N-VA, led by powerful Antwerp mayor Bart De Wever, had made political demands which Michel judged "unacceptable" - notably on possible constitutional changes.
The liberal steadfastly defended the Marrakesh migration pact, saying it presented an "opportunity for better European and international cooperation.
The non-binding UN accord, which would promote a common global approach to migrant flows, was initially supported by all four parties in Belgium's coalition.