The Cambridge City Council last night voted to hold a public hearing next month to discuss disposal of radioactive and other hazardous wastes generated by laboratories at Harvard and the Massachusetts Institute of Technology (MIT).

The Council's motion, introduced by City Councilor Alfred E. Vellucci, represents a series of state and local efforts to tackle the problems associated with waste disposal.

The recent shutdown of Harvard's--and the nation's--only low-level waste dumping site has spotlighted the situation.

Many officials think the only permanent solution to the problem would be to establish regional dumping sites or on-site incineration facilities.

But dumping radioactive wastes is a sensitive political issue, especially in a city like Cambridge, where a controversy over safeguarding the public from recombinant DNA experiments erupted several years ago.

"The City of Cambridge may very well be on the verge of a crisis of major proportions," Vellucci, the onetime leader of the movement to ban DNA research, said yesterday, adding that Harvard has only found "stop-gap" solutions to the problem.

"We have to do this to protect every chick and child in Cambridge," Vellucci said at last night's council meeting.

Harvard, which generated about 100,000 gallons of low-level radioactive waste in 1978, will be forced to cut back on research which generates such wastes this week, unless the University's radioactive dumping site is reopened.

Washington Gov. Dixy Lee Ray closed the Hanford, Wash., dumping site October 4, citing violations of safety procedures in transporting the wastes.

While the situation in Harvard-affiliated teaching hospitals is abnormal, "there is currently no major problem," a medical area source said yesterday.

Murray M. Bolton Jr., radiation safety officer at MIT, said recently MIT has waste storage facilities for about two months, adding that no cutbacks in experiments have been planned.

Joe B. Wyatt, Harvard's vice-president for administration, said yesterday he is not surprised by Velluci's motion. "It is an issue of national proportions," he said, adding, "It's also close to an election in Cambridge, which seems to stimulate interests."

Dr. Warren E.C. Wacker, director of University Health Services, said yesterday the major danger is not the waste's radioactivity but its flammability.

Spokesman for the Massachusetts General Hospital said yesterday they have asked doctors who can delay waste-generating experiments to cut back research but added that MGH faces no immediate crisis.