Khandan said in a Facebook post Tuesday that the couple were screened for coronavirus when they went to the hospital for Nasrin's cardiological test.
"Today, it has been announced Nasrin's test was positive and my result has not come yet," the post read.
Sotoudeh is well known for representing human rights defenders, dissidents and women who protested against the compulsory wearing of a headscarf in Iran.
The human rights lawyer was temporarily released from Gharchak Prison on Saturday in the city of Varamin, south of Tehran, due to deteriorating health, according to the Center for Human Rights in Iran (CHRI).
Sotoudeh is serving a 38-year sentence, 12 years of which she must fulfill before becoming eligible for parole, according to previous CNN reporting citing her family.