Noboa has asked voters to back joint police-military patrols, the extradition of wanted criminals and longer sentences for terrorism and murder, among other crimes, to fight rising violence attributed to drug trafficking gangs.
Polling has suggested voters are more likely than not to support Noboa, 36, in the 11-question referendum although recent power cuts may dampen support.
Five of the measures would modify the constitution if passed.
"The result of this referendum will define the course of the policy we will take," Noboa said at an inauguration event launching the vote.
"As governors we will be obliged to abide by this."
By 10am, eight per cent of voters had come to the polling booths, according to Ecuador's CNE electoral council.
There were difficulties in setting up some polling stations due to heavy rainfall in parts of the country.
Cocaine-smuggling gangs have expanded into every corner of Latin America over the last decade, turning once-tranquil countries like Ecuador into new battlegrounds, security officials and diplomats say.
In January, violence in Ecuador captured world attention when gunmen stormed a live television broadcast and scores of prison staff were taken hostage.
Rafaella Jaramillo, a student from the country's largest city Guayaquil, said on Sunday she planned to vote in favour in order to "cut the legs out" from under crime.
"We want a radical change in our country's security and the referendum is a strong weapon to fight against crime," the 23-year-old said.
Voters will also weigh whether there should be tougher gun controls in areas close to prisons, no parole for crimes like kidnapping or terrorism financing, among others, and whether the military should be able to use confiscated weapons.
The referendum also includes a measure which would allow workers to be contracted by the hour, which opponents say will benefit the rich and international companies, and another recognising international arbitrage.
Some voters were sceptical.
Guayaquil-based teacher Susana Giraldo, 30, said she believed the referendum would not solve security overnight and was being used as a method to pass laws in favour of companies and the rich.
Passing the hourly contract law would be "a crime for poor Ecuadoreans," she said.
"There are some questions that seem to be for private interests and others that wouldn't serve the country at all," student Adriel Jacome, 20, said on Thursday.
Noboa ordered daily hours-long power cuts this week amid drought-related energy shortages, which some pollsters have said could harm his image and potentially the "yes" vote.
Most of Ecuador's energy is from hydropower.
