The fire broke out in a baroque confessional in the cathedral in the early afternoon but was stopped by two "brave" visitors who rushed to pour holy water onto the blaze, local police said in a statement.
Police believe the fire started when a candle placed inside the confessional set alight a curtain. The blaze then spread to the wooden seat of the confessional.
The fire, thought to have been deliberately lit, caused damages worth ten of thousands of Swiss francs to the historic object, police said.
They are now seeking witnesses.
The Cathedral and Abbey of St Gall is a Unesco World Heritage Site and its famous library is a treasure trove of medieval knowledge.