The attacks follow a recent operation by Hamas, which controls Gaza, against militants linked to IS.
One of the bombers who carried out Tuesday’s attacks had previously been held, a security source told the BBC.
A state of emergency was declared after the attacks with forces on alert.
Two police officers were killed and a third Palestinian wounded in the first bomb, which was set off from a motorcycle near a police check point.
The second explosion, less than an hour later, killed another officer and wounded several people at a separate checkpoint, Hamas’s interior ministry said.
- Palestinian territories profile
Security forces deployed hundreds of personnel on the main roads in the Gaza Strip following the attacks.
Hamas has faced periodic internal opposition from more hardline Islamist militants – including those affiliated with IS – and it recently released members of extremist factions as a gesture of goodwill.
Hamas wrenched control of Gaza from the Palestinian Authority President, Mahmoud Abbas, during a civil war in 2007.