The warning by the UN chief was given during an emergency session of the United Nations Security Council, just blocks from where Mr Maduro and his wife Cilia Flores were facing a Manhattan judge.
Before the UN's most powerful body, both allies and adversaries blasted President Donald Trump's intervention and him signalling the possibility of expanding military action to countries like Colombia and Mexico over drug trafficking accusations.
In his statement, Mr Guterres warned that the US's capture of Mr Maduro could trigger greater instability in Venezuela and the wider region.
"I am deeply concerned about the possible intensification of instability in the country, the potential impact on the region, and the precedent it may set for how relations between and among states are conducted," he said in a statement delivered by UN political affairs chief Rosemary DiCarlo.
Mr Guterres called on all Venezuelan actors to engage in an inclusive and democratic dialogue, adding: "I welcome and am ready to support all efforts aimed at assisting Venezuelans in finding a peaceful way forward."
Colombia, backed by Russia and China, requested the meeting of the 15-member council, diplomats said, where representatives from all three countries condemned Saturday's US military operation.
US ambassador Mike Waltz hit back, saying the United States "successfully carried out a surgical law enforcement operation" against what he described as "two indicted fugitives of American justice".
"There is no war against Venezuela or its people. We are not occupying a country," he said.
