New USA head coach Emma Hayes named her 18-player squad for the tournament and there was no place for the 34-year-old, who has scored 123 goals in 224 appearances for the national side.
Hayes opted for Trinity Rodman, Jaedyn Shaw, Sophia Smith and Mallory Swanson as her main forward options in the squad which is looking to secure a fifth Olympic gold and a first since 2012.
Morgan was part of the USA team which won gold at the London Games in 2012 and was also a key part of the 2015 and 2019 World Cup winning teams.
"I'm disappointed about not having the opportunity to represent our country on the Olympic stage. This will always be a tournament that is close to my heart and I take immense pride any time I put on the crest," Morgan said in a social media post.
"In less than a month, I look forward to supporting this team and cheering them on alongside the rest of our country," she added.
'A lovely person'
Hayes said that Morgan was an "amazing player and human" and said it had been a tough decision.
"I've only had one opportunity to work with her in the last camp and I saw firsthand not just her qualities but her professionalism and her record speaks for itself," she said.
"It's not easy making a decision when there's only 16 outfield players and two goalkeepers on a roster of 18 so it was a tough decision of course.
"Especially considering Alex's history and record with this team, but I felt I wanted to go in another direction and selected other players," she added.
The forward had initially been left out of the USA team for the recent CONCACAF W Gold Cup campaign but was a late call-up as a replacement after injuries.
Hayes, who is English, took charge of the USA side last month after finishing her hugely successful spell with Chelsea.
Korbin Albert, the 20-year-old midfielder who came under fire after controversial social media posts on LGBT issues, was selected in the squad.
"I think she has had a really tough time and that has shown in her performances....she's a young person and having to deal with a lot of criticism, rightfully so," said Hayes who said the Paris Saint-Germain player had been selected on merit.
"But I can say firsthand, having spent a limited time with Korbin, that she really is a lovely person," added Hayes, who said Albert was "spending time working on herself".
"I want the fans to really embrace Korbin because I do think she is a tremendous human being," she added.
Before heading to France, the USA will play friendlies against Mexico in New Jersey on July 13 and then three days later Costa Rica in Washington D.C.
At the Olympics, the USA have been drawn in Group B where they will face Zambia, Germany and Australia.
Full squad:
Goalkeepers: Casey Murphy (North Carolina Courage), Alyssa Naeher (Chicago Red Stars)
Defenders: Tierna Davidson (Gotham FC), Emily Fox (Arsenal), Naomi Girma (San Diego Wave), Casey Krueger (Washington Spirit), Jenna Nighswonger (Gotham FC), Emily Sonnett (Gotham FC)
Midfielders: Korbin Albert (PSG), Sam Coffey (Portland Thorns FC), Lindsey Horan (Lyon), Rose Lavelle (Gotham FC), Catarina Macario (Chelsea)
Forwards: Crystal Dunn (Gotham FC), Trinity Rodman (Washington Spirit), Jaedyn Shaw (San Diego Wave), Sophia Smith (Portland Thorns), Mallory Swanson (Chicago Red Stars)
Reserves:
