De Minaur, the top-ranked Australian men's player, returned a positive test for the virus in Spain -- where he lives -- earlier this week, according to local media.
The Australia team comprises six men and five women, including former US Open champion Sam Stosur who will be going to her fifth Olympic Games at the age of 37.
Barty came through 6-1, 6-7 (1/7), 6-1 against Carla Suarez Navarro in a match filled with emotion on Centre Court, whose roof ensured the match could be finished.
Ranked 43 in the world, former French Open champion Ostapenko was handed a wildcard to the Wimbledon warm-up event and could be a contender at the All England Club where she was a semi-finalist in 2018.
Former French Open champion Ostapenko, now 43rd in the world rankings, struck 38 winners against Kazakhstan's Rybakina, who appeared to be hindered late in the first set by a back problem.
The 25-year-old Italian has yet to drop a set on his debut at Queen's and although Australian number one De Minaur gave him a good workout he had too much power for his opponent.
The top-seeded Italian made light of the day's play being delayed by four hours due to torrential rain and exposed the gap between him and the British number one once he came through a tough first set.
Nadal's path to a possible sixth Madrid title was cleared of second seeded Daniil Medvedev and fourth-seeded Monte Carlo champion Stefanos Tsitsipas who were both shock third round losers.
US Open champion Thiem, playing his first tournament since Dubai in March, will meet Andrey Rublev or John Isner in the last eight.
Harris, who beat world number four Dominic Thiem and Denis Shapovalov en route to the final in Dubai in March, pulled off another upset by ousting Dimitrov 6-3, 3-6, 7-6 (7/5).
The world number three triumphed 6-0, 2-6, 6-2 over 2014 and 2015 champion Nishikori and next faces Britain's Cameron Norrie, a fellow left-hander, for a place in the semi-finals.
Gasquet saved the only break point he faced and converted three of his own to become just the sixth active player to reach the 550 mark.
The 20-time Grand Slam champion was due to take the court against Australia's top-ranked player Alex De Minaur, but opted to rest instead as he prepares for the Australian Open next week.
Rafael Nadal kicks off his season representing Spain at the ATP Cup from Tuesday.
The fourth-seeded De Minaur led the eighth seed 2-0 in the first set when his Kazakh opponent retired due to a right ankle injury he suffered in his semi-final.
Serena Williams came from a set down to overcome unseeded Bulgarian Tsvetana Pironkova and keep alive her bid for a 24th singles Grand Slam title at US Open.
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Dominic Thiem, the losing finalist in the Australian Open this year, battled to a 6-2, 6-2, 3-6, 6-3 victory in the late match at an empty Arthur Ashe stadium.
Unranked Bulgarian Tsvetana Pironkova caused her second upset of the week at US Open, knocking out 18th seed Donna Vekic in straight sets.
Kyrgios has a left wrist injury that forced him out of a tournament in Mexico this week while de Minaur has aggravated an abdominal injury which sidelined him for last month's Australian Open.