He was also fined $20,000 for verbally abusing an official and failing to leave the court in a timely manner following an ejection.
At 20-37, the Kings are slightly behind the Lakers (19-39) when considering the NBA draft lottery to be held May 20.
Neither the Lakers nor the Kings are playoff bound. The lower a team finishes in the standings, the greater chance they have at a top-three pick in the June 26 draft.
The Lakers should have the advantage over the Kings with Cousins out, which in turn works to Sacramento's advantage when considering lottery position.
Currently the Lakers have lost three straight and have six wins in the 26 games played since the start of 2014.
Cousins has averaged 22.3 points and 11.5 rebounds a game this season for the Kings.