The explosion came hours after a ceasefire ended a fierce flare-up in fighting between Israel and Hamas resistance movement.
“An explosion took place this morning in a house west of Gaza City,” police spokesman Ayman al-Batnijiy said. He gave their ages as 35 and 13, Reuters reported.
“The police launched an investigation into the cause of the explosion.”
Israel carried out dozens of airstrikes against the Palestinian enclave on Saturday and, in retaliation, Hamas fired more than 100 rockets across the border.
Two Palestinian teenagers were killed by the regime.
Palestinians in Gaza have for months been demonstrating against Israel's decade-long blockade of the territory and in support of their right to return to lands they fled or were driven from during the war surrounding the creation of the Zionist regime in 1948.
In fresh violence Friday, a 15-year-old was shot dead during the demonstrations and a 20-year-old died later of gunshot wounds sustained during the protest, the Gaza health ministry said.
Since the protests and clashes broke out along the border on March 30, at least 141 Palestinians have been killed by Israeli fire.
No Israelis have been killed, but officials said one soldier was injured by a grenade on Friday.