A car bomb exploded today in Banbridge, a mostly Protestant town 22 miles southwest of Belfast, wounding 35 people and shattering shop windows.

None of the injuries were serious. No one immediately claimed responsibility, but the police said there had been a warning and the area was being cleared when the device exploded outside a shoe store.

The blast, caused by 500 pounds of explosives, obliterated the vehicle and damaged shops up and down the street, the police said.

''Many people could have been killed or seriously injured by this terrorist attack, and it is only through the speedy and efficient action by the security forces that a tragedy has been averted,'' said Britain's Northern Ireland Secretary, Mo Mowlam, who visited the blast area this evening.

Irish Republican Army dissidents opposed to the group's cease-fire and operating as the Continuity I.R.A. have carried out several bombings.

Buildings in Banbridge suffered blast damage in April 1994 from a bomb hidden inside a van.