Video of the incident shows Martinez shaking hands with the four umpires before saying something to get him ejected.
The spat likely stems from Tuesday night's game, as plate umpire Doug Eddings came under fire for some questionable ball and strike calls. Blue Jays pitching coach Pete Walker was ejected in that game, a 7-6 win by the White Sox.
After being ejected on Wednesday, Martinez could be seen arguing face-to-face with Eddings before leaving the field.
The Blue Jays went on to defeat the White Sox 9-5.