Cousins missed Thursday night's 116-109 loss to Miami. The Kings are now 11-38 when Cousins does not play, including 0-5 this season.
"He's one of the best bigs in the NBA, so I'd have liked to take that challenge on and really compete against him," said Heat center Hassan Whiteside, who played 18 games with Cousins as teammates with the Kings in parts of two seasons in 2010-12.
Said Heat coach Erik Spoelstra: "Obviously, they were missing a major piece of what they do."
The NBA announced the penalty a day after Cousins and Horford tangled late in the first quarter at Atlanta.
"It was basically a reaction. I was trying to get him off me because when I shot the shot I [got hit] in this area," Cousins, 25, told reporters, pointing to his neck and collarbone. "I was just trying to get him off."
The 6-foot-11 Cousins has averaged 27.5 points and 11 rebounds this season in eight games for the Kings. He has missed four games because of a strained right Achilles.
Cousins, who made the All-Star team last season, is no stranger to NBA discipline.
He sat out last season's finale for his 16th technical foul. He had needed the NBA to rescind a technical foul in each of the previous two seasons to avoid the automatic suspension.
He drew three suspensions two seasons ago, including one by the Kings for "unprofessional behavior and conduct detrimental to the team" after he shouted at then-coach Keith Smart in the locker room during halftime of a loss at the Los Angeles Clippers.
Information from The Associated Press and ESPN Stats & Information was used in this report.