It will be Garcia's first missed major since the 1999 US Open.
"After 21 years of not missing a Major Championship, I will sadly miss The Masters this week," the Spaniard wrote on Twitter on Monday.
"The important thing is that my family and I are feeling good. We'll come back stronger and give the green jacket a go next April.
"On Saturday night after driving back from the Houston Open, I started feeling a bit of a sore throat and a cough. The symptoms stayed with me on Sunday morning so I decided to get tested for COVID-19 and so did my wife Angela. Thankfully she tested negative, but I didn't."
The 2020 Masters, which was postponed from it's usual April slot because of the coronavirus pandemic, will begin on Thursday.
Garcia last played in the first two rounds of the Houston Open last weekend. He failed to make the cut.
The event was the first on the PGA Tour in the US to allow fans back on-site.
"Our hearts and prayers go out to Sergio and his family and we will miss him greatly," Fred S. Ridley, chairman of the Augusta National Golf Club and the Masters Tournament, said in a press conference on Monday. "One of our great former winners here at The Masters."
Honoring a legend
In Ridley's pre-Masters press conference, he announced that the tournament will honor Lee Elder, the first Black man to compete in the Masters.
Elder first competed in The Masters in 1975 and would later qualify for five consecutive years between 1977 and 1981. His best finish came in 1979, when he tied for 17th place.
As well as announcing that Elder would be an Honorary Starter for the 85th Masters Tournament in April, 2021 alongside Gary Player and Jack Nicklaus -- a moment that will "recognize his courageous life and commemorate all he has done in his career to help eliminate barriers and inspire Black men and women in the game of golf and beyond" according to Ridley -- the chairman of Augusta National Golf Club revealed the creation scholarships at Paine College, a Historically Black College and University located in Augusta.
The two scholarships will be awarded annually, one each to a student athlete who competes on the men's and women's golf team. The Masters will also fund the creation of a women's golf program at Paine College.
"The opportunity to earn an invitation to the Masters and stand at that first tee was my dream, and to have it come true in 1975 remains one of the greatest highlights of my career and life," Elder said. "So to be invited back to the first tee one more time to join Jack and Gary for next year's Masters means the world to me.
"It also gives me great pride to know that my first Masters appearance continues to make a positive impact on others. Throughout my career, helping young men and women achieve their dreams through education has been a cause close to my heart. I am deeply honored to share a connection with Paine College and these scholarships, which will provide life-changing opportunities for the deserving recipients."