Embolo’s issue comes after a Swiss court ruling linked to a 2018 altercation in Basel became final nine months ago.
The Stade Rennais striker was convicted in 2023 of making multiple threats and handed a suspended fine, a verdict upheld on appeal after judges rejected his account of the incident. Swiss media reported in April that Embolo had decided not to take the case to the Federal Court, making the judgment final.
"Unfortunately, Breel Embolo is currently unable to travel to the United States with the team," the Swiss federation said in a statement.
"His ESTA authorisation had been approved until this morning. However, at 10:30 a.m., we were informed that his ESTA application had been placed under further review.
"We are currently in contact with the relevant authorities and expect that Breel will either join the team later today or travel tomorrow and join the squad then."
A spokesperson for the team, who were boarding their plane to Los Angeles, told Reuters that Switzerland had previously travelled to the US to play Mexico and the USA, and that Embolo had been allowed into the country.
They are in World Cup Group B with co-hosts Canada, Bosnia & Herzegovina and Qatar. Their opening match is on June 13th against Qatar.