The Labour MP called out to journalists who had to leave the event in central London in order to get to Leadsom’s last-minute press conference.
The former Shadow Business Secretary is challenging Corbyn for the leadership after scores of Labour MPs resigned from his shadow cabinet.
Eagle sought to take questions from the crowd, naming political journalists such as Robert Peston and Michael Crick, but only silence followed.
The awkward clip is being shared on social media, but many people appreciate that it was just an unfortunate issue of timing.
Peston apologised to Eagle for having to “run away from your launch”, adding: “You will understand why.”
At the launch Eagle said that the country was facing a crisis in the wake of the Brexit vote and needed a strong Labour party that was up to the task.
“Jeremy Corbyn is unable to provide the leadership,” she said.
“I will not stand back and allow Britain to become a one party Tory state. We owe too much to the millions in our country who look to us to help them make a better life.”
In a bid to unite the party, she added: “I’m not a Blairite. I’m not a Brownite. I’m not a Corbynista. I am my own woman. A strong Labour woman.”
Eagle was told at the launch that Leadsom had pulled out of the Tory leadership race.
When asked why she could beat Theresa May in a general election, Eagle replied: “Because she’s a Tory.”
Leadsom pulled out of the Conservative Party leadership race on Monday, citing “the interests of our country”.
Her decision to quit the race follows a weekend of headlines dominated by her comments about May not having children.
Leadsom’s departure leaves the Home Secretary unopposed in the contest to replace David Cameron as prime minister.
In a statement in central London, Leadsom said the country needed a new leader “as soon as possible”.
May will be formally confirmed as the new party leader as soon as the Conservative Party board has been consulted, Graham Brady, the chairman of the Tory backbench 1922 Committee, has said, although he refused to give an exact timetable.