Timothy Russell and Malissa Williams died in 2012 in a barrage of bullets fired by 13 officers in a car chase.
Michael Brelo, 31, the only officer to be charged, was cleared of voluntary manslaughter at the court in Cleveland.
The US has seen a series of police race-related killings, some of which have led to serious civil unrest.
In Cleveland itself, the police shooting last November of a 12-year-old black boy, Tamir Rice, as he waved a replica firearm, fuelled the national debate over police use of deadly force.
The ruling has caused anger in the community but protests held after the verdict have been peaceful.
Protesters gathered outside the cordoned-off courthouse, some chanting, "Hands up, don't shoot!"
They later marched from the courthouse to the recreation centre where Tamir Rice was shot.
Some 200 people also held a mock funeral procession in the city, carrying a black coffin and singing to mark six months since the shooting of Tamir Rice. Some held signs that said: "Will I be next?"
Analysis: BBC North America correspondent Rajini Vaidyanathan
The dramatic car chase that ultimately led to the deaths of Timothy Russell and Malissa Williams happened more than two years ago, but many are hearing their story for the first time.
Police shootings aren't uncommon, but events in Ferguson and more recently Baltimore have propelled these issues to the top of the agenda, forcing America to take a long hard look at the way it handles these cases. In this instance, the judge decided to acquit Michael Brelo - a conviction required a burden of proof he believed wasn't there.
But recent protests on the streets of Cleveland show that campaigners are keeping up momentum in raising the wider issues of police brutality. Earlier this week activists took to the streets to highlight the number of black women victims of police violence. The #SayHerName #BlackWomenMatter campaign is designed to raise awareness of black female victims, who don't always attract the same level of media attention.
Police Chief Calvin Williams vowed to support peaceful protest but warned the city would not tolerate violence.
The case involving the deaths of Russell, 43, and Williams, 30, had sparked a department of justice inquiry that concluded Cleveland police had engaged in a pattern of excessive force and violation of civil rights.
Only Mr Brelo was charged because prosecutors said the pair in the car were no longer a threat when he climbed on to the bonnet of their car and fired 15 shots through the windscreen in 7.4 seconds.
But the judge said that as other officers had fired in a 137-shot barrage, he could not rule beyond reasonable doubt that Mr Brelo was responsible for the deaths.
Cuyahoga County Common Pleas Judge John O'Donnell also cleared Mr Brelo of the lesser count of felonious assault.
The judge said he would not "sacrifice" Mr Brelo if the evidence did not warrant conviction.
"Guilty or not guilty, the verdict should be no cause for a civilised society to celebrate or riot," he said.
County prosecutor Timothy McGinty said he was "profoundly disappointed" with the verdict.
Russell's sister, Michele, said Mr Brelo would not "dodge this just because he was acquitted. God will have the final say."
Mr Brelo had faced up to 22 years in jail if convicted of voluntary manslaughter.
The incident occurred when the car, a Chevy Malibu, backfired while speeding past Cleveland police HQ, and officers thought a gun had been discharged.
Some 62 police cars were then involved in a 22-mile chase at speeds up to 100 mph.
Both Russell and Williams had previous convictions and a crack pipe was found in the car.
Mr Brelo's lawyer, Patrick D'Angelo, said his client had risked his life during the chase and that the prosecution of the case was "vicious and unprofessional".
There have been a number of deaths at the hands of police in the US that have sparked race-related protests.
The two most serious were in Ferguson, Missouri, and in Baltimore.
In April, Freddie Gray died in hospital a week after Baltimore police had taken him into custody.
His death sparked weeks of protests and later riots and looting in the city.
In Ferguson, teenager Michael Brown was killed last August by a white police officer. Protests followed, and there was further unrest after a grand jury decided not to charge the officer.
A US policeman who climbed on to a car bonnet and fired repeatedly through the windscreen at unarmed black occupants has been cleared of all charges.