The House Social Security subcommittee tentatively approved a phaseout of the student benefit and the $122-a-month minimum benefit yesterday as it began work on a bill to keep the Social Security system solvent.

President Regan had requested elimination of the student benefit and the minimum guarantee in order to save about $2 billion a year to strengthen the troubled system. But the subcommittee watered down both provisions so that the initial saving will be about $450 million a year.

The subcommittee tentatively agreed to make the minimum benefit elimination prospective for those coming on the rolls after Dec. 31 instead of retroactive to all 3 million persons already receiving the minimum, as Reagan wanted.

The subcommittee also agreed that student benefits would continue to be available for anyone starting college by January 1983. Reagan wanted to cut them out faster.

Next week the subcommittee will take up more fundamental proposals such as raising the retirement age to 68, funding half of Medicare from general revenues, eliminating restrictions on what retirees can earn and reducing the annual cost-of-living increases in benefits.

Meanwhile, Secretary of Health and Human Services Richard S. Schweiker told a House Commerce subcommittee that administration plans to give the states more flexibility in handling Medicaid funds would include the right to take away the Medicaid patient's freedom of choice of doctor and hospital.

Schweiker said the states would be authorized to sign fixed-cost medical service agreements with group health organizations, hospitals and other providers of medical services and then require the patient to obtain care from those providers. Schweiker added that it was conceivable that similar loss of freedom of choice of doctor and hospital would eventually be written into the Medicare program. "I don't rule that out," he said.