Budget director David A. Stockman has ordered deep cuts in federal health agencies for next fiscal year, including 20 percent personnel reductions for both the Food and Drug Administration and the Centers for Disease Control, it was learned yesterday.

Those are two of the main federal agencies involved in protection of the public health.

The CDC cut would occur in one year, the FDA cut over three.

The orders are contained in a budget document sent by Stockman's Office of Management and Budget to the Department of Health and Human Services on Nov. 23. A copy was obtained by The Washington Post yesterday.

Similar documents have been sent to other departments for the fiscal 1984 budget that President Reagan will send to Congress early next year. The White House has already indicated that that budget will involve deep further cuts in domestic spending programs, on top of those Reagan pushed through Congress in each of the last two years.

Reagan has said he does not want either to increase taxes or to moderate his defense buildup, which means that almost all the burden of holding down the deficit will fall on the domestic side of the ledger.

Indications from both parties are that Congress will resist large further cuts, however, and the OMB orders can also still be appealed to the president by HHS Secretary Richard S. Schweiker. Schweiker successfully appealed some cuts last year; aides would not say what he might do now.

The budget documents indicate that the OMB wants both the CDC and FDA to start charging "user fees" to offset some of the contemplated cuts in government funds. The National Institutes of Health would be required to start charging room and board to patients at its research center in Bethesda.

The OMB, according to the documents, has told HHS to dismantle its Alcohol, Drug Abuse and Mental Health Administration and disperse its functions to other agencies.

In addition, most of the functions and personnel in the office of the assistant secretary for health would be shifted to other agencies and the assistant secretary would be cut to a small staff concerned solely with broad policy decisions.

The OMB is also proposing personnel and money cuts for the Indian Health Service and a number of other public health agencies including St. Elizabeths Hospital here.

In some cases, the funding and personnel levels would be below the actual dollar levels contemplated by Congress for fiscal 1983.

Sources said that in addition to cuts in public health programs, the OMB wants to cut personnel in the direct administrative offices of Schweiker from 4,000 to 3,000, wiping out a large batch of budget, personnel and public affairs jobs, and to cut personnel sharply in the Office of Human Development Services.

However, the OMB has apparently approved a Schweiker request of about $1 billion for the Head Start program, making no attempt to cut it. Last year, Schweiker appealed an OMB attempt to cut Head Start and won.

This is what the budget document contemplated for the various programs of the Public Health Service, the HHS unit containing FDA, CDC and the other affected agencies:

* The Public Health Service as a whole would have a budget of $7.3 billion for the fiscal year starting next Oct. 1, $500 million less than Schweiker requested.

* The FDA, operating on a $349 million budget this year, would be frozen at the same dollar level despite inflation, and its personnel would be cut to 7,063, or 6 percent below the request and several hundred below the actual 1983 figure; added personnel cuts coming eventually to nearly 20 percent are contemplated by OMB, sources said.

* The CDC, which the documents indicate Congress has so far provided with $318 million and 4,162 personnel in 1983, would be cut in fiscal 1984 to $215 million and 3,401 personnel under the OMB proposal.

* The National Health Service Corps, which provides personnel for public health facilities, now at $93 million, would drop to $75 million and personnel cut by one-third to 1,400, with new doctors encouraged to use the private practice option.

* The Indian Health Service, now at a program level of $683 million with 10,526 full-time equivalent personnel, would be cut $13 million and lose 200 personnel; the PHS had requested a slight increase.

* Schweiker requested a slight fiscal 1984 increase for the National Institutes of Health over the tentative level of $4.1 billion for fiscal 1983. The OMB pared this to $4 billion, allowing no inflation increase, and proposed keeping personnel at 13,405.

* St. Elizabeths Hospital, for which Schweiker asked 3,300 jobs and $62 million, would be cut to 3,000 jobs and $50 million, plus $7.4 million from an alcohol, drug abuse and mental health grant.

* Programs on smoking and health, health promotion, physical fitness and health education loans would lose money, personnel or both.