The 20-year-old was named in the 35-man provisional squad on Friday having expressed his desire to play in the competition, which begins on August 3.
With the 2016/17 Premier League season starting on August 13, Iwobi faced missing Arsenal's first fixture against Liverpool and potentially Leicester on the following weekend.
A source close to Iwobi told the website: "Arsenal have taken a decision on Alex, he will not be going to the Olympics with Nigeria.
Arsenal's Most Expensive Transfers
"The boy himself is very disappointed because he wanted to be in Rio but Arsenal have the final say on this matter because the competition is not on the FIFA calendar.
"They want him to start the new season with them."
Iwobi enjoyed a breakthrough campaign last season, impressing for the Gunners as they finished second in the table.
We use your sign-up to provide content in ways you've consented to and to improve our understanding of you. This may include adverts from us and 3rd parties based on our understanding. You can unsubscribe at any time. Read our Privacy Policy