The games had been set to begin in Orlando, Florida, but participants had to make due with a video conference with Biden and Prince Harry, and a scaled down virtual competition.
"There was a call to defend the values we hold dear as we waged a global war on terror and a courageous group of men and women stepped forward to say: 'Me, I will go'. And that includes you, Harry, you live by a simple principle, serve together, recover together," Jill Biden said at the event.
The games, which involve a variety of sports and promote the rehabilitation of wounded active duty and military veterans, debuted in 2010.
Prince Harry, a military veteran who did two tours of duty in Afghanistan, was inspired by the games to found a similar competition, the Invictus Games, in 2014.
"To see every single one of you here with the pride on your faces makes me incredibly happy to know how far you guys have come, the dark places that you've been to, but where you are now stronger than ever before, no doubt. And that is partly, if not mainly down to sport," Prince Harry said to the participants taking part in the virtual event.
Retired Staff Sergeant Joel Rodriguez, a control tower operator who suffered a spinal chord injury in 2014, competed in multiple competitions, including the 2018 Invictus Games in Sydney, Australia.
Rodriguez said he and his fellow competitors would not be deterred by this year's cancellation.
"We are still fighting out there, we are still competing and, you know I've talked to my teammates and I said for them to just continuously train that everybody will come back stronger, it will be better, and the next games will be incredible," he said.