No one was injured, but the grenade explosions shattered several months of relative calm in the Ain al-Hilwah camp near Sidon.
One bomb targeted an office of Palestinian President Yasir Arafat's Fatah faction, while the other hit a residential area.
Lebanon executed three men in Beirut's Roumieh prison on Saturday, despite objections by human rights groups and the European Union.
These were the first executions in the country in five years.
Badia Hamadah, who was killed by firing squad, was convicted of killing three security officers in a raid in 2002 and was believed to have links to Usbat al-Ansar group, which Washington deems "terrorist" and is based in the camp.
Hamadah later fled to Ain al-Hilwah, which is beyond the reach of Lebanese authorities.
Following a four-day manhunt, Palestinian factions controlling the refugee camp brokered his arrest.
His handover fuelled tensions in the camp, sparking clashes between Hamadah's supporters and Palestinian factions including Fatah, which played a key role in the arrest.
Palestinian sources said they now expected more explosions in the camp.
Hamadah was buried in a cemetery in Sidon on Saturday, but authorities refused to allow a public funeral procession out of security concerns.
Lebanese politicians are generally hostile to Lebanon's roughly 390,000 Palestinian refugees for fear of tipping the state's delicate sectarian balance.
They also point to Ain al-Hilwah as a haven for trouble-makers and organised criminals.