John Alexander Milligan (January 22, 1904 – May 15, 1972) was a pitcher in Major League Baseball who played from 1928 through 1934 for the Philadelphia Phillies (1928–1931) and Washington Senators (1934). Listed at 5 ft 10 in (1.78 m), 172 lb., Milligan batted left-handed and threw right-handed. A native of Schuylerville, New York, he attended Cornell University.
In a five-season career, Mulligan posted a 3–8 record with 38 strikeouts and a 5.17 ERA in 35 appearances, including 12 starts, four complete games and 116+2⁄3 innings of work.
Milligan died at the age of 68 in Fort Pierce, Florida.