The hurricane is drenching the Louisiana city exactly seven years after the devastating Hurricane Katrina, but is much less powerful.
The city has closed its new floodgates in a bid to protect it from the effects of high waters brought by sustained winds of up to 80mph (130km/h).
Sea water has already breached a levee in a town to the south of the city.
Caitlin Campbell, a spokeswoman for Plaquemines Parish - where Isaac first touched down - said water was running over an 18-mile (29-km) stretch of the levee and some homes were flooded.
After hitting Plaquemines Parish, the Category One hurricane headed back out to sea, before making a second landfall further west at Port Fourchon at about 02:00 (07:00 GMT) local time.
There are now reports of serious flooding and people stranded by rising waters in the Braithwaite area, just across the Mississippi river from metropolitan New Orleans.
Waiting out the storm At 08:00 local time, the centre of the storm was 40 miles south of New Orleans and moving inland at about 6 mph, according to the US National Hurricane Center (NHC).

Officials are urging residents who have not evacuated to stay in place until high winds dissipate.
"We have resources ready to go, but until the winds come down, we're really asking people, if you're not somewhere that's dangerous, stay where you're at unless you're told to evacuate," Federal Emergency Management Agency director Craig Fugate told CNN.
About a half-million people were without power in Louisiana as of Wednesday morning, and two highways north of New Orleans were no longer passable because of storm surge.
Isaac killed at least 24 people as it passed over Haiti and the Dominican Republic earlier this week.
It has also caused significant flooding and damage across the Caribbean and forced a day's delay to the start of the Republican party's congress in Tampa, Florida.
Braithwaite flooding The overtopped eight foot levee to the east of Plaquemines Parish is not part of the upgraded federal system protecting New Orleans after Hurricane Katrina.
Braithwaite, on the eastern bank of the Mississippi, appeared to be the hardest hit by severe flooding.
The community of around 1,800 people lies just outside the new defensive wall.
Plaquemines president Billy Nungesser told NPR the damage wrought in the parish by Isaac was worse than Katrina.

"Not only did we see the worst case scenario, it got worse than that by this storm just stalling," he later told CNN, adding that the parish had been in the process of upgrading its own levee system.
Mr Nungesser said water levels in the area were 12 to 14 feet, and there were 25 people trapped in attics or roofs, with 65 others on a rescue list.
Strong winds were hampering full-scale air and water rescue efforts in the area, but the BBC's Alastair Leithead reports local residents were trying to make rescues with small boats. National Guard was also set to launch a rescue effort.
In New Orleans, the updated levees appeared to be holding as the city was lashed by rain and winds.
"We don't expect a Katrina-like event, but remember there are things about a Category One storm that can kill you," said New Orleans Mayor Mitch Landrieu on Tuesday.
But storm surges are still a concern, with peaks of up to 12ft (3.7m) forecast in parts of Mississippi and south-eastern Louisiana. Rainfalls of up to 1ft 8in are forecast across wide areas, along with a high chance of isolated tornadoes along the coast.
The bowl-shaped city of New Orleans is particularly vulnerable to storms, with the centre of the city the furthest below sea-level.
But Mr Landrieu said that the 26ft-high levee gate which now protects the areas of the city that were badly flooded in 2005 had been closed since Tuesday morning.
Many residents of New Orleans have chosen to secure their homes but stay put, saying they were not too concerned by Isaac.
"I feel safe," said Pamela Young from her home in the Lower Ninth Ward, a neighbourhood devastated by Katrina.

"Everybody's talking 'going, going', but the thing is, when you go, there's no telling what will happen. The storm isn't going to just hit here.
"If the wind isn't too rough, I can stay right here. If the water comes up, I can go upstairs."
President Barack Obama has declared an emergency in Louisiana and Mississippi, allowing federal funds to be released to local authorities.
Speaking from the White House, he warned residents along the Gulf Coast to heed warnings, including those to evacuate, saying: "Now is not the time to dismiss official warnings. You need to take this seriously."
Shortly before Isaac reached hurricane status on Tuesday, Louisiana Governor Bobby Jindal said the emergency declaration fell short of the federal help he had asked for.