Virginia Gov. Charles S. Robb underwent apparently successful cataract surgery on his right eye today, the first of two operations planned to correct his longtime vision problems.

Robb's operation, performed at the Medical College of Virginia near the State Capitol, lasted 55 minutes. It was performed by Dr. Robert S. Weinberg, an associate professor of ophthalmology, who said in a statement released by Robb's office that "the governor's surgery was successful" and that Robb was "experiencing no discomfort."

The governor's operation was performed with a local anestheic and Robb, 46, was awake the entire time. He was released at 11:30 a.m. and returned to the governor's mansion, his office said.

Robb, whose mother underwent cataract operations when she was a teen-ager, is scheduled to rest during the Thanksgiving holiday and has no public events planned until Monday. Robb is to travel later in the week to a conference of state government officials in Nevada.

Weinberg's statement said the governor's only restrictions for the next several weeks are to avoid lifting items more than 10 pounds and to avoid bending at the waist -- measures designed to keep excessive pressure off his eyes. Robb "will be given some eyedrops but no other medication," his office said.

Weinberg's surgery -- an intraocular lens implant -- replaced Robb's clouded natural lens with a plastic lens, an increasingly common procedure in recent years that is generally done on an outpatient basis.

Robb has long been troubled by the cataracts, but only within the last year began wearing eyeglasses to compensate for the lost vision. "I'm both blind and vain," Robb said on several occasions. He often required lecterns raised higher than his chest to read documents or speeches in public.

George M. Stoddart, Robb's press secretary, said today Robb is not likely to have surgery on his left eye until after he leaves office Jan. 11.

He postponed his initial surgery partly to allow himself time to play a major role in the campaign of Democratic Gov.-elect Gerald L. Baliles and Baliles' running mates for lieutenant governor and attorney general. Under Virginia law, Robb could not succeed himself.

Robb, who has been mentioned as a potential candidate for national office in 1988, has announced he will become a partner in the 300-member law firm of Hunton & Williams and will maintain personal offices in Fairfax County, Richmond and Norfolk.

Although his precise role in the firm has not been announced, Robb is expected to become involved in lucrative development work and is widely regarded as a "rainmaker" -- a term used by lawyers for influential partners whose contacts or status bring additional business to a firm.

Robb, a founder of the moderate Democratic Leadership Council based in Washington, also has said he would remain active in efforts to bring a moderate image to the national Democratic Party and is expected to campaign for Sunbelt Democrats in the 1986 elections.