The punishments, including fines of an undisclosed amount, were issued before Thursday's final game in a series at Seattle against Detroit with the incident coming in the Mariners' 4-2 triumph Wednesday over the Tigers.
Wilson, who served his suspension in Thursday's contest, and Speier were ejected on Wednesday with MLB saying the bans were a result of Speier's "intentional throwing" at Detroit's Gleyber Torres, who was struck in the left leg in the eighth inning by a 96.3-mph Speier fastball.
It was the second inside fastball in a row to Torres and came an inning after Seattle's Cal Raleigh was hit in the left ribs by a 94.7-mph fastball from Detroit reliever Enmanuel De Jesus.
Speier is appealing his suspension and any discipline will not be imposed until the process is completed.
Bench coach Manny Acta filled in for Wilson serving the first suspension of his career.
"It is what the rule is and not that I agree, but that's where we are," Wilson said.
Mariners starting pitcher Bryan Woo had hit three Tigers batters over his seven shutout innings.
"These things tend to bring guys together," Wilson said. "It tends to cultivate intensity and I think it was a great example of that."