The Interior Ministry earlier confirmed one policeman had been killed in the attack.
"On Saturday, March 24, an explosive device planted underneath a vehicle exploded.as the Alexandria security chief drove by", a spokesperson for the interior ministry said in a statement cited by Reuters.
However, Egypt's state news agency MENA blamed the now-banned Muslim Brotherhood, which the state describes as a terrorist group, following the bombing.
The attack comes just days ahead of Egypt's presidential election, in which President Abdel-Fattah el-Sissi is virtually certain to be re-elected.
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Health ministry spokesman Khaled Megahed said the casualties were taken to a military hospital.
A roadside bomb exploded in Egypt's coastal city of Alexandria today, killing one policeman and injuring four others, two days before the presidential elections.
Prosecutor General Nabil Sadek ordered an "urgent and wide inquiry".
Pictures shared on social media showed smoke billowing from the burned out remains of a vehicle.
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The Islamic State terror organization claimed responsibility for both attacks.
It is also the first major attack in the Mediterranean city since the April 2017 bombing of St Mark's Cathedral, which killed 18 people during Palm Sunday celebrations.
Sisi gave the armed forces and police a three-month deadline in November to wipe out the jihadists.
The president's ultimatum came after suspected IS gunmen massacred more than 300 worshippers in a Sinai mosque associated with Sufi Muslims, who are seen by IS as heretics.
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