LOS ANGELES—Federal agents Tuesday executed search warrants at several Southern California sites they say are connected to three multimillion-dollar birth-tourism businesses that enabled thousands of Chinese women to travel here and return home with infants born as U.S. citizens.

The investigations are likely to culminate in the biggest federal criminal case ever against the booming “anchor baby” industry, according to U.S. authorities. The search warrants cite suspected visa fraud, tax evasion and harboring illegal immigrants,...