"We are all on the mend and doing fine," Rice, a South Carolina Republican, said in a Facebook post.
"We are finishing our quarantine and looking forward to seeing you all again," he added. "Friends, please wash your hands and take precautions. Stay healthy. See you soon."
Six other members of U.S. Congress have also tested positive for the coronavirus and since recovered.
Confirmed cases in many U.S. states have spiked as they are reopening.