A man and two children were electrocuted to death when a cable from a tramway fell into a street flooded with water, the health ministry said in a statement.
And the captain of a ship drowned as he was unable to get out of his car which filled with floodwaters.
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A 25-year-old man was also electrocuted after he fell into a pit full of electric cables.
An AFP photographer said the downpour began in the early morning and quickly flooded several streets in Egypt's second city as well as the corniche.
Temperatures dropped sharply on Sunday across several governorates in Egypt, including Cairo, bringing also heavy rains and strong winds.
Greetings from #Alexandria, #EgyptPosted by Your Middle East on Sunday, 25 October 2015