B

$\because y=\left(x-2\right)^{2}$的顶点坐标为$\left(2,0\right)$，$y=x^{2}$的顶点坐标为$\left(0,0\right)$，
$\therefore$将抛物线$y=x^{2}$向右平移$2$个单位，可得到抛物线$y=\left(x-2\right)^{2}$.
故选：$B$.