Medics and security officials said two policemen were killed in the first explosion while they were on a motorbike.
Ashraf al-Qedra, spokesman for the Health Ministry in Gaza, identified the two, who he said were killed in the "mysterious explosion," as Salama al-Nadeem and Alla’ Gharablai.
The third was identified as Wa'el Khalifa and according to local media he was killed in a second explosion that occurred shortly after the first.
The Interior Ministry said that three others were injured in the explosions, adding that police and security forces were investigating the nature of the two blasts.
No group claimed responsibility for the explosions.
Ministry spokesman Eyad al-Bozzom said a state of emergency was declared following the explosions.
Residents said they heard an Israeli army drone over Gaza city at the time.
Asked for comment on the explosions on Tuesday night, the Israeli army said it was "not aware of any strike tonight."
Hamas, Islamic Jihad, the Popular Front for the Liberation of Palestine and other minor groups accused Israel of being behind the explosions and trying to unsettle the situation in the Gaza Strip.
Earlier Tuesday, an Israeli aircraft targeted a Hamas military post in northern Gaza in response to a projectile fired from the Palestinian coastal enclave into southern Israel.
The European Union, Israel and the United States classify Hamas, which rules Gaza, as a terrorist organization.
Israel imposes a blockade on Gaza's coastal area with Egypt's support. Both countries cite security concerns to justify the measure.
Some 2 million people live in the Gaza Strip in harsh conditions. There is a shortage of drinking water and electricity, among other things.
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