The explosion, which damaged the shop and a neighbouring store in an area controlled by Islamic fighters, came a day after a blast damaged a house and the offices of an official from Palestinian President Yasir Arafat's Fatah group.
It took place at about 4.30am (0130 GMT) on Monday and damaged the gate and staircase of a house belonging to the Mayaleh family.
On Sunday, a separate grenade attack inflicted no casualties.
Eight people were killed in May in a three-day gunfight between Fatah supporters and Islamic fighters in Ain al-Hilwah.
Home to 80,000 refugees, Ain al-Hilwah falls outside the control of the Lebanese army
In total, there are about 390,000 Palestinian refugees registered in a dozen camps across Lebanon.