Nine inmates were transferred from the Fairfax County jail to state corrections facilities Tuesday morning in the Virginia government's first move to comply with a court ruling that Fairfax cannot be forced to hold state prisoners in the crowded county jail.

Under an order by Fairfax Circuit Court Judge William G. Plummer, 60 state inmates must be transferred from the jail to state custody in the next three weeks at a rate of 20 a week to relieve overcrowding. The inmates, convicted in Fairfax courts of violating state laws, have been held in the county jail because state officials have maintained there is no room for them in the prisons.

Terrell Don Hutto, state corrections director, announced after the ruling that the state will appeal the case to the Virginia Supreme Court, but meanwhile will comply with the ruling. The appeal is expected to be an extended process that may take months, according to corrections spokesman Wayne Farrar.

Hutto also said the state would attempt to accommodate 300 to 500 prisoners now in local jails across Virginia within the next several months in order to be fair to other jails that are as crowded as, or more crowded than, Fairfax.

All convicted felons with more than six months to serve in their sentences are considered state prisoners in Virginia. There are about 1,300 such inmates in local jails around the state now, according to officials.

Corrections officials say they are concerned that other localities will follow the Fairfax lead and sue the state to ease conditions in their jammed facilities.

"I don't know if we could take all those prisoners," Farrar said. "I don't know where we'd put that many people."

The state is currently building two 500-bed prisons, in Brunswick and Buckingham counties in southern Virginia. Scheduled to open early n 1983, the prisons are expected to provide some relief for the state's crowded penal system.