The University of Maryland Board of Regents yesterday approved a 9 percent tuition increase for the fall of 1983 after being told by Gov. Harry Hughes that slow growth in tax revenues will limit state aid to the institution.

The increase, approved unanimously at a meeting in College Park, will bring the cost of tuition and required fees next year to $1,292 for undergraduates who are Maryland residents. The cost for out-of-state undergraduates will climb to $3,598. For medical students at the university's Baltimore campus, the tuition and fees will rise to $4,284 for Maryland residents.

The increases follow rises averaging 10 percent for the term that begins late this month and 22 percent last year. They are far greater than the current rate of inflation, which has slowed to about 6 percent a year.

University officials said the major tuition increase for 1973 was necessary because Hughes has approved only a 3.3 percent increase in the $186.6 million that the university is receiving this year in state aid.

"Even with a 9 percent increase in tuition, we are still left with a budget that is less than adequate," said university president John S. Toll. "It's a very tight budget, and the basic reason is the tightness of the economy. We are in a recession period and state revenues are not increasing as much as projected."

David Fram, a senior from Baltimore who is a student representative on the board, said he voted for the tuititon increase because it was necessary to fund a "bare bones budget."

"There have been some huge tuition increases over the past few years," Fram said. "But Maryland still is a good deal, relative to other institutions."

Tuition this year at Maryland is $1,185. At most private colleges in the Washington area, tuition this fall is increasing from 14 to 21 percent, and will range from a low of $4,800 at Mount Vernon College to $6,890 at Georgetown University.

At the University of Virginia tuition and fees this year will come to $1,350, after a 17.8 percent increase. At George Mason University, the figure will be $1,176, after a 16.7 percent rise. The University of District of Columbia continues to have the lowest tuition by far -- $364.

Last month, the board of trustees for Maryland's six state colleges and universities, which are separate from the University of Maryland, approved a 7 percent tuition increase of the fall of 1983. These schools receive only a 2.6 percent increase in state aid under Gov. Hughes' preliminary budget estimates. But over the last decade their tuition has risen far more rapidly than at the University of Maryland, which had only slight increases from 1974 to 1980.

In contrast to most states, Maryland's public colleges now charge more than its major state university.

Donald L. Myers, assistant vice president at the University of Maryland, said tuition at the university covers only about one-third of the cost of a student's education. But he said the effect of the new increase will be to shift a higher proportion of costs onto students and away from taxpayers, a pattern that is taking place nationwide.