Griffith, 62, has been in self-imposed isolation since being tested.
"Although he does not currently have significant symptoms, he will continue to self-isolate as he performs his duties" on behalf of his Virginia district, the statement said.
A member of the House Energy and Commerce Committee, Griffith has participated in hearings and news conferences on Capitol Hill, including an outdoor news conference last week to push for reopening US schools.
House Speaker Nancy Pelosi last month called on committee chairmen to require members to wear masks during proceedings, after a number of Republican lawmakers defied public health recommendations.
Coronavirus cases have recently increased in areas of Virginia outside the Washington suburbs. Griffith represents the state's 9th Congressional District in the southwest, along the state's borders with West Virginia, Kentucky, Tennessee and North Carolina.At least nine other House and Senate members have tested positive for the coronavirus, been presumed by physicians to have the virus or have been shown to possess antibodies to the pathogen.