The former is likely to be known colloquially as the Vinicius law, following an incident in a Champions League game in which Benfica's Gianluca Prestianni covered his mouth when addressing Real Madrid's Vinicius Jr, who accused him of making a racist slur.
The latter follows Senegalese players walking off the pitch during the Africa Cup of Nations final against hosts Morocco.
Both of the FIFA-proposed laws were unanimously approved by the International Football Association Board (IFAB) on Tuesday at a special meeting in Vancouver, Canada.
"At the discretion of the competition organiser, any player covering their mouth in a confrontational situation with an opponent may be sanctioned with a red card," an IFAB statement read.
Prestianni had confronted Vinicius Jr after the Brazilian scored Real Madrid's goal in a 1–0 win in Lisbon.
The incident prompted the referee to activate UEFA's anti-discrimination protocol, halting the match. Argentine winger Prestianni, who denied the accusation, was earlier this month handed a six-match ban (three matches suspended) by UEFA for discriminatory conduct that was deemed homophobic.
Senegal's players had walked off in protest at a last-minute penalty awarded to Morocco in Rabat.
They returned and, after the penalty was missed, scored in extra time to win the game, although they were then stripped of the title after the Confederation of African Football's Appeal Board upheld Morocco's protests.
Morocco were handed a 3-0 victory. Senegal subsequently appealed to the Court of Arbitration for Sport which will hold proceedings next month.
"This new rule will also apply to any team official who incites players to leave the field of play," said IFAB. "A team that causes a match to be abandoned will, in principle, forfeit the match."
