Beginning today, U.S. airlines may fly anywhere in the United States without asking the Federal government for permission.

Under a schedule set by the Airline Deregulation Act of 1978, the Civil Aeronautics Board lost its authority over airline entry to domestic routes at midnight last night. Now, an airline that has been found fit to provide interstate air service may serve any city in the nation without CAB approval.

The Board had been in the domestic route regulation business since 1938. Until the deregulation law was passed, the board was going through a complicated hearing process, averaging 19 months, every time an airline wanted to fly a new route. The board often picked one airline for a route that many airlines wanted to fly, weighing such issues as potential profitability and the effect of a new entrant on the incumbent carriers. Now, an airline will make route decisions on its own and take its chance in the marketplace.

Since 1979, the CAB has been authorizing airlines to serve any market they desired, but the process has been taking up to 60 days. Although airlines can serve any domestic point now without federal involvement, airlines seeking to terminate service at a community still are required to file a notice with the board.

Under other provisions of the deregulation law, the CAB loses all authority over domestic fares at the end of this year, and goes out of existence on Jan. 1, 1985, unless Congress acts to alter the schedule.

In another development yesterday, the CAB acted to block the sale of Wien Air Alaska by Household International Inc. to Eagle International Corp., a $50 million transaction that would have taken place today.

The Eagle-Wien merger is part of a complicated transaction the board said it wants to look at more carefully. Eagle and Alaska International Air, a cargo carrier, are both owned by Neil G. Bergt, who last month was named chairman and chief executive officer of Western Airlines. The board said yesterday the prospect of Bergt's controlling Western, Wien and Alaska International "raises significant concerns about the possible effects on competition in the Alaska cargo industry"--concerns that should be aired and resolved through a normal acquisition proceeding before the board.

Bergt, an Anchorage businessman, had asked the CAB last week for quick approval of the Eagle-Wien purchase under special provisions of the board's regulations. The board said Eagle must file a formal application for approval of its contemplated combination with Wien and ordered Bergt to file an application for approval of his interlocking relationship with Western no later than Jan. 15.

Under Bergt's plan, according to an analysis by Oppenheimer & Co, after Eagle has acquired Wien for $50 million, Western Airlines would acquire Wien from Eagle by the issuance of 5 million new series preferred stock worth about $80 million. If the Western-Wien acquisition is successful, passing CAB Muster, Eagle would gain voting control of 41 percent of Western. The new preferred would have voting rights equal to 12.5 million Western common shares, according to Oppenheimer. Western currently has 13 million common shares outstanding.