At midnight tonight, the Civil Aeronautics Board loses all authority to regulate domestic air fares.

As a result, U.S. airlines tomorrow may begin to set all domestic fares without first asking the government for permission.

Not that the change will be particularly noticeable.

As a practical matter, the CAB already had given the airlines freedom to set their fares within very broad zones of flexibility.

The board said yesterday that the fares on most domestic routes are below the allowable ceilings, an indication that competition has been determining prices.

Control over air fares is the second major chunk of regulation the CAB has lost under the Airline Deregulation Act of 1978.

A year ago, the board lost its authority over the assignment of domestic routes to airlines. As a result, an airline that has been found fit to provide interstate air service may serve any city in the nation without CAB approval.

The airlines' freedom to fly to any city has been limited lately because of continuing restrictions by the Federal Aviation Administration on airspace, as a result of the air traffic controllers' strike last year.

International air fares will continue to be regulated through international agreements.

The CAB itself is scheduled to go out of existence on Jan. 1, 1985, unless Congress alters the timetable.