Broadcaster ABC7 said its reporters had spoken to people at the airport who confirmed the tower would be unstaffed.
The staff said duties at Burbank would be handled by a team in San Diego, which would speak to pilots coming in and going out of the airport.
In a statement to AFP, a spokesperson for the airport said: “operations are continuing”.
“We are advising passengers to check with their airline - before arriving at the airport - for updates on possible delays or cancellations,” the statement said.
The development comes as a nationwide government shutdown enters its second week, with President Donald Trump’s Republican Party at odds with Democrats over how to pay for many of the US Government’s functions.
Most federal workers have been placed on enforced leave and are not being paid during the shutdown.
But those doing jobs considered essential, like air traffic controllers, are expected to continue to work, albeit without pay.
Political commentators have said it is only a matter of time before this system - effectively one of good will - breaks, and staff begin to call in sick while they are not being paid.
Democrats are refusing to provide the votes the ruling Republicans need to reopen federal departments, unless an agreement is reached on extending expiring “Obamacare” healthcare subsidies and reversing some cuts to health programmes passed as part of Trump’s signature “One Big Beautiful Bill”.
The non-partisan Congressional Budget Office estimated the bill, which was signed into law on July 4, would strip 11 million Americans of healthcare coverage, mainly through cuts to the Medicaid programme for low-income families.
That figure would be in addition to the four million Americans whom Democrats say will lose healthcare next year if the health insurance subsidies are not extended - while another 24 million Americans will see their premiums double.
Republicans argue the expiring healthcare subsidies have nothing to do with keeping the government open and can be dealt with separately before the end of the year.
-Agence France-Presse