The flare was let off 15 minutes into the game - which ended 1-1 - after United scored.
Police said it was discharged from the crowd in the away end before hitting the roof and ricocheting back down into the crowd at the Liberty Stadium.
Detectives said it was fortunate that the flare missed any spectators and that no-one was hurt following the incident at about 1.50pm.
Detective Inspector Jeff Handley, of South Wales Police, said: "We are proud of the fact that the Liberty Stadium promotes a family atmosphere and welcomes spectators from all over the UK.
"This was a very foolish act by an irresponsible individual.
"We are fortunate that nobody was seriously hurt today [Sunday].
"It's important that anybody with information contacts us so that we can identify the individual and let him or her explain their actions to a court."
Detectives are appealing for anyone with information to contact South Wales Police.