The Department of Health and Human Services is expected to announce within a few days that the Medicare premium will jump from $17.90 a month this year to $24.80 in 1988 -- an increase of more than one-third, the largest in the program's history.

The premium covers Part B of the program, which pays for doctor bills. Unless there is a last-minute change of plans, sources said yesterday, the increase means that aged and disabled Medicare beneficiaries will have to pay almost $300 a year in premiums.

The department is also planning to announce that the amount a Medicare patient must pay a hospital for his or her first day of hospitalization will rise from $520 this year to $540 in 1988, proportionately a much smaller increase than the boost in the doctor premium.

"I am shocked by this news" of the Part B increase, said Rep. Fortney H. (Pete) Stark (D-Calif.), chairman of the House Ways and Means subcommittee on Medicare. "The impact will be particularly severe for the 50 percent of the elderly with incomes of less than $10,000."

Rep. Henry A. Waxman (D-Calif.), chairman of a House Energy and Commerce subcommittee that has cojurisdiction over Part B, said, "This is certain to spur efforts to reform the way we pay doctors in the Medicare program."

John Rother, legislative director of the American Association of Retired Persons, called the increase "unprecedented. It seems to reflect an out-of-control program where the taxpayers and the Medicare program are writing checks" for the medical profession.

Glenn Hackbarth, the program's deputy administrator, declined to confirm that the Part B premium is increasing to $24.80 per month but said next year's premium would be substantial. Hackbarth attributed the rise to a number of factors, primarily a 20 percent increase in program outlays in one year.

Medicare began in 1965, and now covers about 31 million aged and disabled Social Security recipients. Part A pays for hospital bills, and the recipients do not have to pay premiums. It is financed from a trust fund fueled by the Social Security payroll tax paid by employed people.

However, Part B, which covers doctor bills, is financed by a monthly premium paid by Medicare enrollees, plus payments from the Treasury general revenues. The premiums are designed to cover 25 percent of the Part B costs. It is these premiums that are to be raised to $24.80 a month.

Earlier this year it was estimated that the 1988 Part B premium would be only $22. The new figure has not been formally released by HHS, and some officials reportedly have launched a last-minute search for a way to reduce the $24.80 figure. But the law does not give them much leeway, because for calendar 1988, the premiums are required to cover 25 percent of Part B costs.

The 20 percent increase in Part B costs, Hackbarth said, occurred in part because some services previously performed in hospitals were shifted to doctors' offices. In addition, he said, Medicare-reimbursed doctor fees had been allowed to rise. Still another reason was a 9 percent increase in "intensity" of services (more visits and more costly procedures provided).

He also noted a speedup in Medicare's bill-paying cycle and that the increase will reflect an effort to obtain some margin of financial reserve for Part B. This part of Medicare has been operating recently with no cash reserve, he said.

Stark said yesterday that the increase in Part B indicates that "physician payment under Medicare is badly out of control."

Payments to doctors under the program have been increasing at an annual compounded rate of 17 percent a year, Stark said, and "the problem is that the current fee-for-service payment system gives doctors a key to the Treasury . . . . The only solution to the problem is tight new limits on fees."

Waxman said, "Clearly, we'll have to question the wisdom of following the Reagan administration recommendation to have the elderly pay a premium that is 25 percent of program costs. That can be a lot when trying to live on Social Security."