The incident happened during Sunday's round-12 game at Etihad Stadium and sparked an angry exchange between the two players and incensed Pearce's teammates.
The AFL announced on Monday it had launched an investigation.
Minson will formally apologise to Pearce and Port Adelaide Football Club and undertake education in line with the AFL's Respect and Responsibility Policy, the Bulldogs added in a statement.
"The club has the highest of expectations when it comes to players' behaviour both on and off the field," Bulldogs' chief executive Simon Garlick said.
"While Will is genuinely remorseful for his actions, the club will not tolerate the use of inappropriate and offensive comments, especially in regards to women."
Minson said there was no excuse for his behaviour, which reportedly included a reference to Pearce's mother.
"I sincerely apologise for my comments and regret they have caused hurt and offence to Danyle, his family and the Port Adelaide Football Club," Minson said.
"I realise there are no excuses for my behaviour and I accept the sanction given to me by the club."
AFL General Manager Football Operations Adrian Anderson on Tuesday said the league commended the Western Bulldogs for taking strong action over the on-field exchange.
He said the AFL endorsed the club's decision to suspend Minson for one match, for him to issue a formal apology to Pearce and to be part of a compulsory education session around the game's Respect and Responsibility Policy with AFL Cultural Strategy and Education Manager Sue Clark.
Anderson said he was pleased Minson acknowledged his behaviour did not meet the standards expected across the competition and that he was apologetic for what had occurred.
"All players, coaches and officials across our competition are aware that there is no place within our game for comments that are offensive and demeaning towards women."