They were shot dead behind closed doors, security sources said.
"To achieve public deterrence and curb crime, the competent authorities carried out at dawn on Tuesday, May 31, 2016 execution rulings against three of those convicted of shocking murders," a statement from the attorney general said.
In theory all execution orders in the Palestinian territories must be approved by president Mahmud Abbas, who is based in the occupied West Bank.
But Hamas, the militant Islamist group that runs the Gaza Strip, no longer recognises his legitimacy, and Gaza attorney general Ismail Jaber recently announced that the authorities there would carry out the executions without Abbas's backing.
Xavier Abu Eid, a spokesman for the Palestinian Liberation Organisation, immediately condemned the executions on Twitter.
Sari Bashi, Israel and Palestine director at Human Rights Watch, said Hamas authorities had been under pressure to act due to perceptions of increased crime in Gaza, including a number of grisly murders of civilians.
"This is an attempt by the government to show they are doing something," she told AFP, "but killing criminals is not going to decrease crime."
She urged Israel to ease the 10-year blockade on Gaza and called for rival Palestinian factions to come together.
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"These people were convicted in a judicial system where torture and coercion are common," she added.
The attorney general's statement announcing the executions said the three men had all been given a fair trial.
The UN envoy for the Middle East, Nickolay Mladenov, had called on Hamas to abandon the planned executions.
Jaber had initially said that he wanted executions to be carried out in public. It was unclear if that would happen in the future.
At the time of the attorney general's announcement last week, 13 men, most convicted of murder connected to robberies, were awaiting execution.
The last public executions in Gaza were during the 2014 war with Israel when a firing squad from Hamas's armed wing shot dead six alleged collaborators with Israel in front of Gaza City's main mosque following prayers.
According to the Palestinian Centre for Human Rights (PCHR), nine death sentences were handed down in the Gaza Strip in 2015 and two in the occupied West Bank, run by the Palestinian Authority.
So far this year, around 10 more people have been sentenced to death in Gaza.
Palestinian law allows the death penalty for collaborators, murderers and drug traffickers.
Of the more than 170 Palestinians sentenced to death since the creation of the Palestinian Authority in 1994, around 30 have been executed, mostly in Gaza, according to the PCHR.