Hamas' interior ministry said two deaths occurred after the first explosion.
Scarcely an hour later, a second blast occurred across town on a main coastal road, killing another officer. There, blood stains covered the road and debris from a damaged law enforcement trailer was scattered about. Police were deployed heavily in the area, blocking the street and directing traffic as ambulances arrived on the scene to take the body away.
It wasn't immediately clear who was responsible for the attacks.
But the deadly blasts are reminiscent of previous bloody rounds of infighting between Hamas and more radical Salafi groups which believe the militant group is too lenient in imposing Islamic norms on society.
Hamas chief Ismail Haniyeh stressed that Gaza can "absorb" such incidents.
"We are certain things will be controlled and all sides involved in these bombings will be held accountable," he said in a statement.
Immediately after the first blast, Hamas' health ministry spokesman blamed Israel, but later deleted his statement on Twitter. The Israeli military said it was unaware of any action in the Gaza Strip.
The blasts came amid rising tensions following Israeli restrictions on the gas supply to the Palestinian enclave after rocket fire at southern Israel.