Embolo missed the team's departure to California on Tuesday after his ESTA travel authorisation was placed under further review hours before the squad boarded their flight to Los Angeles.
"The Embassy informed us that the application is being processed as a priority," the federation said in a statement on Wednesday.
"Breel and the team are now awaiting approval so that he can travel to San Diego and join the squad as soon as possible."
The issue relates to a legal case stemming from a 2018 altercation in Basel. The Rennes striker was convicted in 2023 of making multiple threats and handed a suspended fine, a verdict later upheld on appeal.
The federation said U.S. authorities had requested court documents linked to the case after learning that the judgement had become final and legally binding earlier this year.
"The Embassy's inquiries focused specifically on whether any physical violence had been involved. This was not the case," the federation added.
According to the Swiss federation, all ESTA applications, including Embolo's, had initially been marked as approved before U.S. authorities requested additional checks roughly two and a half hours before departure.
"The Trump administration is enforcing immigration laws," Assistant Secretary for Public Affairs at the U.S. Department of Homeland Security (DHS) Lauren Bis told Reuters.
"Under the Visa Waiver Program, all ESTA applications are continuously vetted against law enforcement and security databases. Travelers must provide complete and truthful information, including all criminal history.
"Failure to disclose arrests or convictions constitutes misrepresentation and can lead to ESTA denial, revocation, or a permanent bar from entering the United States. An approved ESTA does not guarantee admission. Individuals ineligible for the VWP due to criminal convictions or misrepresentation must apply for a visa."
A Swiss team spokesperson told Reuters on Tuesday that Embolo had previously travelled to the United States with the national team in June 2025 for matches against Mexico and the United States without issue.
Switzerland are in World Cup Group B alongside co-hosts Canada, Bosnia and Qatar. They open their campaign against Qatar on June 13 in San Francisco.