Hathaway spit on Gudbranson in the second period of the Capitals' 5-2 win over the Ducks on Monday, earning an ejection.
"That's about as low as you dig a pit, really," Gudbranson told reporters. "It's a bad thing to do. It's something you just don't do in a game, and he did it."
Hathaway said his actions were "wrong" and attributed them to a heat of the moment reaction to being "sucker punched."
"Unfortunately, spit came out of my mouth after I got sucker-punched, and it went onto him," Hathaway said. "It has no place. It was an emotional play by me. You don't plan any of that stuff in your head, and it was a quick reaction and unfortunately the wrong one for me to a sucker punch."
The suspension will result in Hathaway forfeiting $24,193.53 in salary. He will be eligible to return for next Friday's home game against the Tampa Bay Lightning.
The Capitals were already one of the NHL's most shorthanded teams due to injury. It's unclear what the team will do over this three-game stretch to replace Hathaway, who has registered seven points in 23 games this season.