"This win is dedicated to them," Guardiola told reporters at the Etihad Stadium, in response to a question on the matter from a Spanish journalist.
"We have shown in Catalonia that citizenship is bigger than any ideas. We hope they will be released soon."
Tens of thousands of people took to the streets of Barcelona on Tuesday to protest against the Madrid-based National Court's ruling to keep Jordi Cuixart and Jordi Sanchez behind bars pending investigations into sedition charges.
Guardiola, a Catalan, is one of the most famous figures associated with Barcelona Football Club, having won multiple trophies there as both player and coach.