The Times of Malta has reported it happened last night in an area just off Libyan waters, 120 miles south of Lampedusa.
It has been reported that 28 migrants have been rescued so but hundreds are feared dead.
The Italian coastguard and navy are continuing to search for survivors.
The boat is believed to have overturned when migrants moved to one side of the overcrowded vessel as a merchant ship approached in the sea.
Maltese Prime Minister Joseph Muscat said that many people were feared dead:
@Armed_Forces_MT assisting rescue op after boat wt 650 immigrants capsized in #Libya waters. Less than 50 rescued so far. Many feared dead.
— Joseph Muscat (@JosephMuscat_JM) April 19, 2015
Amnesty International UK director Kate Allen said: "Yet again we have woken up to reports of another tragedy in the Mediterranean, which could bring the total number of migrants who've drowned just this year to a shocking 1,500.
"This is a Europe-wide crisis that needs a Europe-wide response. How many more will have to drown before EU governments, including the UK, wake up to their responsibilities to save lives?
"In the run up to the UK general election, now is the time for all UK political parties to commit to supporting an effective EU-led search-and-rescue operation."
