The blasts hit a district dominated by supporters of Hamas and disrupted celebrations for the Muslim Eid el Fitr holiday.
The targeted groups issued a joint statement condemning the attackers as "traitors" – suggesting they thought the perpetrators were fellow Palestinians – and promising that they would be "found and punished".
No one claimed responsibility, but Hamas, which dominates the coastal enclave, has in recent months faced violent challenges from Palestinians sympathetic to Islamic State or al Qaeda, and who seek stringent religious rule in Gaza and open war with Israel.
Palestinian sources said security officials suspected the attacks were triggered by timers placed near explosives planted in and near the vehicles.
Salafists claiming allegiance to Islamic State have begun launching rockets at Israel in defiance of Hamas' truce with the Jewish state since a war a year ago in which 2,100 Palestinians and 73 Israelis were killed.
Last month Islamic State militants fighting Egyptian forces in neighbouring Sinai released a video threatening to turn Gaza into another "fiefdom" as in parts of Iraq and Syria.
Palestinians seek a state in East Jerusalem, the West Bank and the Gaza Strip, territories Israel captured in the 1967 Middle East war.