The Texas lawmaker “passed away peacefully” with his wife Susan by his side on Sunday, his office said.
The couple had both been infected with the virus and were receiving treatment at Baylor Hospital in Dallas.
Mr Wright, who had also been battling cancer in recent years, is the first sitting member of Congress to die with the coronavirus.
On 21 January, he released a statement announcing that he had tested positive for Covid-19.
“I am experiencing minor symptoms, but overall, I feel okay and will continue working for the people of the 6th [Congressional district] from home,” his statement said.
Mr Wright was elected to the House of Representatives in 2018.
Announcing his death on Monday, his office said that he would be “remembered as a constitutional conservative” who was “a statesman, not an ideologue”.
“Despite years of painful, sometimes debilitating treatment for cancer, Ron never lacked the desire to get up and go to work, to motivate those around him, or to offer fatherly advice,” it added.
The office provided no further details.
JUST IN: Republican Rep. Ron Wright of Texas has died, his congressional office announces, saying that he had been admitted to the hospital after contracting Covid-19. https://t.co/lyzapNqAsc— CNN (@CNN) February 8, 2021
Several members of Congress, from both the House of Representatives and the Senate, have tested positive for Covid-19 over the past year.
In December, 41-year-old Congressman-elect Luke Letlow died due to complications from the coronavirus, just days before he was due to be sworn in.
The US is by far the world’s worst-hit nation, with more than 463,000 coronavirus-related deaths and over 27 million cases since the start of the pandemic.
The average number of daily infections in the US, however, has been gradually falling since early January.