The 22-year-old, who is on a season-long loan at Turkish side Kasimpasa from Chelsea, has been told by the team doctor he needs time to recover.
"I feel sad about it as it was another good opportunity for me to represent my country," Omeruo told BBC Sport.
"The doctor insists I need rest to start next season without injury."
Omeruo was first called up by Nigeria in January 2013 and he went on to play at that year's Africa Cup of Nations and Confederations Cup - and at the 2014 World Cup.
He admitted he was looking forward to playing at the Games, especially after the Super Eagles' failure to qualify for the 2015 and 2017 African Cup of Nations.
"It is disappointing and frustrating to say the least. I'd be lying if I said I would not want to be out there playing," he said.
"But at the same time I need to be fully fit to be at my best and I have no doubt that the squad will do great in Brazil.
"I would also like to thank the coach [Samson Siasia] for even considering me in the first place."
A firm fixture in the Kasimpasa side, such has been Omeruo's impact that the Turkish club are now exploring the option to buy him at the end of his loan spell.
He joined Chelsea from Belgian side Standard Liege in 2012 and developed on loan at ADO Den Haag in Netherlands in an 18-month spell from 2012 to 2013.
The centre-back, who is yet to make his competitive debut for Chelsea, then went on loan to Championship side Middlesbrough in January 2014 and made 14 appearances.
He returned to Teesside again for the whole of 2014/15 season where he made 22 appearances.
Nigeria international defender Kenneth Omeruo has been declared unavailable to play at the 2016 Olympic Games in Rio because of a groin problem.