The incident occurred in the away end after Patrice Evra had given the visitors the lead over their Welsh hosts, who would eventually equalise before half-time through Michu.
The flare is said by police to have hit the stadium's roof before bouncing back into the crowd. Fortunately, no supporter was injured.
"We are proud of the fact that the Liberty Stadium promotes a family atmosphere and welcomes spectators from all over the UK," Detective Inspector Jeff Handley of South Wales Police told reporters.
"This was a very foolish act by an irresponsible individual and we are fortunate that nobody was seriously hurt today.
"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."The incident marks the second consecutive home game that police have been involved at the Liberty Stadium, after allegations of racism towards Norwich City defender Sebastien Bassong in his side's 4-3 victory over hosts Swansea.