Xinhua news agency says Alimu Ahbudurimu was convicted of evading taxes worth $26,000.
His brother, Kahaer Ahbudurimu, was also found guilty of tax evasion but spared a jail term.
Kadeer, the mother of 11, is a leading figure in the movement to defend the rights of the Uyghur people, a Turkic-speaking Muslim minority in northwestern China that is believed to number about 8 million. Uyghur populations are also present in Kazakhstan, Kyrgyzstan, Uzbekistan, Mongolia, and Turkey.
Kadeer was jailed for five years for having given state secrets to foreigners before being sent into exile in the United States in 2005.